Download ch 7 arithmetic progression

1.
∑
√
can be written as
(a) √ + √ + √
+√
(b) √ + √ + √
+ √
(c) √ + √ + √
+ √
(d) None of these
2.
2, 5, 8, 11, 14, 17... is an A.P in which the common difference is?
(a) 2
(b) 3
(c) -2
(d) -3
3.
Determine the common difference of progression 16, 13, 10 ......... 25 terms
(a) 2
(b) -2
(c) 3
(d) -3
4.
Two A.Ps have the same common difference. If the difference between their 100th terms is
111222333 then the difference between their millionth terms is
(a) 123
(b) 112233
(c) 111222333
(d) 112333
5.
If a, b, c are in A.P., then 2b = ____
(a) a – c
(b) a + b
(c)
(d)
6.
If the terms 2x, (x+10) and (3x+2) be in AP, the value of x is...
(a) 7
(b) 10
(c) 6
(d) None of these
7.
The value of x such that 8x+4, 6x-2,2x+7 will form an A.P. is
(a) 15
(b) 2
(c) 15
(d) None of these
8.
Find the 7th term of the A.P 8, 5, 2, -1, -4, …
(a) -13
(b) -10
(c) -7
(d) -16
9.
The 20th term of the progression 1, 4, 7, 10 is…..
(a) 58
(b) 52
(c) 0
(d) None of these
10.
For the A.P 2, 5, 8, 11, 14, .... , 12th term is(a) 34
(b) 33
(c) 35
(d) 36
11.
The 13th term of series 93, 90, 87.... is
(a) 57
(b) - 54
(c) 50
(d) 54
12.
The nth element of the sequence 1,3,5,7,.... is
(a) n
(b) 2n -1
(c) 2n +1
(d) None of these
13.
The nth term of the sequence 2, 4, 6, 8….. is
(a) 2n
(b) 2n-1
(c) 2n + 1
(d) N
14.
If the first term of an AP. is 5 and its 100th term is -292, then its 51st term is –
(a) -142
(b) -149
(c) 155
(d) -145
15.
The mth term of an A.P is n and nth term is m, the rth term of it is
(a) m + r + r
(b) n + m - 2r
(c) m - 2r
(d) m + n - r. 16.
16.
If the p term of an AP is q and if term is p, the value of the (p+q)th term is
(a) 0
(b) 1
(c) -1
(d) None
17.
If the 5th and 12th terms of the A.P are 14 and 35 respectively, find the A.P.
(a) -2, 2, 6, 10, 14, ...
(b) -10, -4, 2, 8, 14, ...
(c) 6, 8, 10, 12, 14, ...
(d) 2, 5, 8,11, 14, ...
18.
Which term of the A. P 11, 8, 5,2 ,... is -10?
(a) 10th
(b) 8th
(c) 12th
(d) 14th
19.
Which term of the progression -1, -3, -5, .... is -39?
(a) 21st
(b) 20th
(c) 19th
(d) None of these
20.
Which term of the A.P
√
,
√
,
√
,….. is
√
?
(a) 13
(b) 14
(c) 15
(d) 16
21.
The last term of the series 5,7,9,….. to 21 term is
(a) 44
(b) 43
(c) 45
(d) None of these
22.
The last term of the A.P 0.6,1.2,1.8 to 13 term is
(a) 8.7
(b) 7.8
(c) 7.7
(d) None of these
23.
Determine the first term of an A.P. with common difference 3 & 7th term being 11
(a) -7
(b) 7
(c) 6
(d) 5
24.
Find three numbers in AP whose sum is 6 and the product is -24
(a) -2, 2, 6
(b) -1, 1, 3
(c) 1, 3, 5
(d) 1, 4, 7
25.
If the 10th term of an A.P. is twice the 4th term, and the 23rd term is ‘k’ times the 8th term, then
the value of 'k' is
(a) 2.5
(b) 3
(c) 3.5
(d) 4
26.
The sum of________________ between the actual values and the AM is zero.
(a) sums
(b) differences
(c) product
(d) square root
27.
The A. M between 2 & 4 is(a) 2
(b) 4
(c) 3
(d) 6
28. The arithmetic mean between 8 & 20 is(a) 6
(b) 12
(c) 14
(d) 18
29.
The two arithmetic means between -6 and 14 is
(a) ,
(b) ,
(c)
,-
(d) None of these
30.
The 4 arithmetic means between -2 and 23 are
(a) 3,13,8,18
(b) 18,3,8,13
(c) 3,8,13,18
(d) None of these
31.
The Arithmetic mean between 5 and 13 is
(a) 9
(b) 10
(c) 8
(d) None of these
32.
The arithmetic mean between 33 and 77 is
(a) 50
(b) 45
(c) 55
(d) None of these
33.
The arithmetic mean between a & c is(a) ac
(b)
(c)
(d)
34.
If the AM of two numbers is 6 and GM is 6 then find the numbers.
(a) 6, 6
(b) 10, 8
(c) 10, 6
(d) 9, 2
35.
Between the two numbers whose sum is , an even number of A.M is inserted. If the sum of
arithmetic mean exceeds their number by unity, then number of arithmetic means inserted are –
(a) 6
(b) 10
(c) 8
(d) 12
36.
The sum of progression (a+b), a, (a-b) n term is
(a) [2a + (n-1)b]
(b) [2a + (3 - n)b]
(c) [2a + (3 - n)]
(d) [2a (n -1)]
37.
The second term of an A.P. is a2 its common difference is 'd'. Then the sum of its first 'n’ terms is
(a) [2a2 + (n - 1)d]
(b) [2a1 + (n + )d]
(c) [2a2 + (n - 3)d]
(d) [a2 + (n -1)d]
38.
The sum of the series 1+2+4+8+ .... to 10 term is
(a) 1024
(b) 1023
(c) 1025
(d) None of these
39.
The sum of series 8,4,0….. to 50 terms is
(a) 18900
(b) 9000
(c) -4500
(d) None of these
40.
The sum of the series 3 +7+10 +14+…. to 17 terms is
(a) 530
(b) 535
(c) 535
(d) None of these
41.
The sum of all numbers between 200 and 300
(a) 11,600
(b) 12,490
(c) 12,500
(d) 24,750
42.
The sum 1+2+3+4 +70 is equal to
(a) 2484
(b) 2485
(c) 2845
(d) None of these
43.
The sum of series 8, 4, 0…. to 50 terms is
(a) 18900
(b) 9000
(c) -4500
(d) None of these
44.
Find the sum of first twenty five terms of AP series whose nth term is (
)
(a) 105
(b) 115
(c) 125
(d) 135
45.
The sum of an A.P. whose first term is - 4 and the last term is 146 is 7171. Find the Value of n.
(a) 99
(b) 101
(c) 100
(d) 102
46.
The sum of the series 1 + 2 + 3 + 4 +……. + 100 is
(a)
(b) *
+2
(c) 100 x 101
(d) None el these
47.
The maximum sum of the A.P. series 40,36,32 .... is
(a) 220
(b) 225
(c) 232
(d) 320
48.
The sum of
and
(a)
(b)
(c)
(d)
49.
+
(a) a - b
(b) a + b
=…..
is
(c) a2 – b2
(d) 1
50.
The 8 th term of the progression 8, 5, 2, -1, -4, is (a) -12
(b) -13
(c) 13
(d) 12
51.
The 10th term from the end of the A.P. 4,9,14,…. 254.
(a) 204
(b) -209
(c) 209
(d) 214
52.
The sum of a series in AP is 72 the first term being 17 and the common difference -2. the number
of terms is___
(a) 6
(b) 12
(c) 6 or 12
(d) None
53.
The number of terms in the series 1+ 3 +5 +7 +….+ 61 is(a) 30
(b) 28
(c) 31
(d) 29
54.
The number of the terms of the series 10+9 3 + 9 + 9.... will amount to 155 is
(a) 30
(b) 31
(c) 32
(d) None of these
55.
The sum of certain numbers of terms of an AP series -6, -3, 0 is 225. The number of terms is
(a) 16
(b) 15
(c) 14
(d) 13
56.
How many terms are there in the A.P. whose first and fifth terms and -14 and 2 respectively and
the sum of the term is 40 ?
(a) 2 x Common Difference
(b) 10
(c) 8
(d) 14
57.
The number of terms in the A.P. 7, 13, 19,….97 is
(a) 97
(b) 17
(c) 16
(d) 15
58.
The Pth term of an AP is
The sum of the first n terms of the AP is
(a) n(3n+1)
(b)
(3n+1)
(c)
(3n-1)
(d) None of these
59.
The sum of all natural numbers from 100 to 300 which are divisible by 4 and 5 is
(a) 10200
(b) 30000
(c) 8200
(d) 2200
60.
The sum of all natural numbers from 100 to 300 which are divisible by 5 is (a) 10200
(b) 30000
(c) 8200
(d) 2200
61.
The sum of all natural numbers from 100 to 300 which are divisible by 4 and 5 is
(a) 10200
(b) 30000
(c) 8200
(d) 2200
62.
The sum of n terms of two APs are in the ratio of
equal
. Then the__ term of the two series are
(a) 12
(b) 6
(c) 3
(d) None
63.
The sum of the first 100 terms common to the series 17, 21, 25 .... And 16, 21, 26,..: is
(a) 202200
(b) 100101
(c) 101010
(d) 101100
64.
If the Pth term of an AP is q and the qth term is p the value of the rth terms is
(a) p – q – r
(b) p + q – r
(c) p + q + r
(d) None
65. The pth term of an AP is and the qth term is The sum of the pq term is
(a) (pq+1)
(b) (pq-1) 2
(c) (pq+1)
(d) (pq-1)
66.
The sum of p terms of an AP is q and the sum of q terms is p. The sum of p+q terms is
(a) -(p+q)
(b) (p+q)
(C) (p-q)2
(d) P2–q2
67.
If S1, S2, S3 be respectively the sum of n, 2n, 3n terms of an AP the value of S3 ÷(S2-S1) is given by
(a) 1
(b) 2
(c) 3
(d) None
68.
If S1, S2, S3 be the sums of n terms of three APs the first term of each being unity and the
respective, common differences 1 2 3 then
is
(a) 1
(b) 2
(c) -1
(d) None
69.
If the nth terms of two A.Ps are in the ratio (3n+1):(n+4) the ratio of the fourth term is
(a) 2
(b) 3
(c) 4
(d) None
70.
The sum of 'n' terms of two A.Ps are in the ratio of
(a) 32:59
(b) 1:1
. The ratio of their sixth terms is
(c) 2:1
(d) 5:11
71.
If m, p, q are comsecutive terms in an A.P. then p is –
(a)
(b)
(c) 2(m2 + q2)
(d)
72.
The five numbers in AP with their sum 25 and the sum of their squares 135 are
(a) 3, 4, 5, 6, 7
(b) 3, 3.5, 4, 4.5, 5
(c) -3, -4, -5, -6, -7
(d) -2, -3.5, -4, -4.5, -5
73.
Three numbers are in A.P. whose sum is 69 and the product of first two is 483. Numbers are
(a) 25, 23, 21
(b) 21, 23, 25
(c) 19, 22, 25
(d) None of these
74.
Three numbers are in A.P. of whose sum is 15 and whose product is 105, then numbers are:
(a) 3, 5, 7
(b) 2, 5, 8
(c) 0, 5,10
(d) None of these
75.
The three number in AP whose sum is 27 and the sum of their squares is 341 are
(a) 2, 9, 16
(b) 16, 9, 2
(c) Both (a) and (b)
(d) -2, -9, -16
76.
The four numbers in AP whose sum is 24 and their product is 945 are
(a) 3, 5, 7, 9
(b) 2, 4, 6, 8
(c) 5, 9, 13, 17
(d) None
77.
The four numbers in AP whose sum is 20 and the sum of their squares is 120 are
(a) 3, 5, 7, 9
(b) 2, 4, 6, 8
(c) 5, 9, 13, 17
(d) None
78.
The four numbers in AP with the sum of second and third being 22 and the product of the first
and fourth being 85 are
(a) 3, 5, 7, 9
(b) 2, 4, 6, 8
(c) 5, 9, 13, 17
(d) None
79.
Divide 69 into three parts which are in A.P and are such.that the product of the r two parts is
483.
(a) 21, 23, 25
(b) 23, 25, 27
(c) 19, 21, 23
(d) 17, 19, 21
80.
Sum of three numbers in A.P. is 12 and the sum of their cube is 408. The numbers are
(a) 3, 4, 5
(b) 1, 4, 7
(c) 2, 4, 6
(d) None of these
81.
The five numbers in AP with the sum 20 and product of the first and last 15 are
(a) 3, 4, 5, 6, 7
(b) 3, 3.5, 4, 4.5, 5
(c) -3, -4, -5, -6, -7
(d) -2, -3.5, -4, -4.5, -5
82.
Find the four numbers in A.P. with the sum of second and third being 22 and the product of the
first and fourth being 85.
(a) 3, 5, 7, 9
(b) 2, 4, 6, 8
(c) 5, 9, 13, 17
(d) None of these.
83.
In a certain arithmetic sequence, if the 24th term is twice the 10th term, then 72nd term is twice
the –
(a) 30th term
(b) 40th term
(c) 34th term
(d) 38th term
84.
Divide 12.50 in five parts in AP such that the first part and the last part are in the ratio 2:3
(a) 2, 2.25, 2.5, 2.75, 3
(b) -2, -2.25, -2.5, -2.75, -3
(c) 4, 4.5, 5, 5.5, 6
(d) -4, - 4.5, -5, -5.5, -6
85.
If sum of first 50 natural numbers is 1275 and the sum of first 50 odd numbers is 2500, then the
sum of the first 50 even numbers is
(a) 2550
(b) 1275
(c) 1725
(d) 2500
86.
In an A.P. if the sum of first n term is Sm=n2p and sum of first m terms is Sm=m2p where m, n, p
are positive integers and m ≠ n, then Sp is .......
(a) n2Sp
(b)
(c) (m2 + n2)p
(d) p3
87.
The number of numbers between 74 and 25556 divisible by 5 is
(a) 5090
(b) 5097
(c) 5095
(d) None of these
88.
The sum of all natural numbers between 500 and 1000 which are divisible by 13
(a) 28405
(b) 24805
(c) 28540
(d) None of these
89.
The sum et three integers in AP is 15 and their product is 80. the Integers are
(a) 2,5,8
(b) 8,5,2
(c) 2,8,5
(d) Both (a) and (b)
90. The sum of all natural numbers from 100 to 300 which are exactly divisible by 4 or 5 is
(a) 10200
(b) 15200
(c) 16200
(d) None of these
91.
The first term of an AP is 14 and the sum of the first five terms and the first ten terms are equal
is magnitude but opposite in sign. The term of the AP is
(a) 6
(b) 6
(c)
(d) None of these
92. Find the number which should be added to the sum of any number of terms of the AP so that the
resultant is also an AP
(a) -1 .
(b) 0
(c) 1
(d) None
93.
If unit is added to the sum of any number of terms of the AP 3,5,7,9,... the resulting sum is
(a) 'a' perfect cube
(b) 'a' perfect square
(c) 'a' number
(d) None of these
94.
In an Ashoka Chakra, the central angle made by the smallest sector, two small sectors, three
small sectors and so on are....
(a) In A.P.
(b) Equal
(c) In G.P.
(d) Such that their summation is 3600
95.
A person employed in a company at Rs. 3000 per , month and he would get an increase of Rs. 100
per year. Find the total amount which he receives in 25 years and the monthly salary in the last
year.
(a) 1380000 and 6200
(b) 930000 and 5400
(c) 1480000 and 7200
(d) 1570000 and 4800
96.
A person pays Rs. 975 by monthly installment each less then the former by Rs. 5. the first
installment is Rs. 100. The time by which the entire, amount will be paid is
(a) 10 months
(b) 15 months
(c) 14 months
(d) Norte of these
97.
A person saves Rs. 16,500 in ten years. In each year after the first year he saved Rs. 100 more
than he did in the preceding year. The amount of money he saved in the 1st year was
(a) Rs. 1000
(b) Rs. 1500
(c) Rs. 1200
(d) None of these
98.
Water flows into a tank. The volume of water in the tank at each minute form an A.P. if the initial
volume was 5 litres and becomes 6 times after 6 minutes. The speed of water increase is
(a) 5 ltr./min
(b) 6 Itr./min
(c) 15 Itr./min
(d) 2 Itr./min