Download 1) Use the arithmetic sequence of numbers 2, 4, 6

1)
Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a)
what is d, the difference between any two consecutive terms?
Answer:
The common difference, d, can be found by subtracting the first term from the
second term
add 2 to each term to arrive at the next term,
or...the difference a2 - a1 is 2.
So
d=2
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?
Answer:
To find any term of an arithmetic sequence:
where a1 is the first term of the sequence , d is the common difference, n is the
number of the term to find.
n = 101; a1 =2, d = 2
a101=2+(101-1)2
a 101 = 2+(100)2 =202
So the 101st term is
202
c) Using the formula for the sum of an arithmetic sequence, what is the sum of the
first 20 terms?
Answer:
The common difference d for the sequence is 2.
The first term a is 2.
The number of terms is 20.
Substituting a = 2, d = 2, n = 20 in the formula for the sum of n terms
Sn 
20
(2 * 2  (20  1)2)  420
2
Sn =420
d)
Using the formula for the sum of an arithmetic sequence, what is the sum of
the first 30 terms?
Answer: a=2,d=2 and n=30
S n
30
(2(2)  (30  1)2  930
2
Sn =930
e)
What observation can you make about the successive partial sums of this
sequence (HINT: It would be beneficial to find a few more sums like the sum of the
first 2, then the first 3, etc.)?
Answer:
2+4 = 6
4+6 =10
6+8 =14
8+10=18
Every sum is larger than the previous and the difference between sums is growing
by4
2)
Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a)
What is r, the ratio between 2 consecutive terms?
Answer: The common ratio, r, can be found by dividing the second term by the first
term
Here second term=3 and first term =1
so r=
3
3
1
The ratio
r=3