Download Arithmetic Sequences

Arithmetic Sequences
March 20, 2017
Arithmetic Sequences
Arithmetic Sequences
How would you find the hundredth term (a100) of the arithmetic sequence?
term
sequence
a1 a2 a3 a4
15...
11
7
3
1
Arithmetic Sequences
March 20, 2017
Arithmetic Sequences
How would you find the hundredth term (a100) of the arithmetic sequence?
Term
Sequence Term
Term
Number
1
2
3
4
a1
a2
a3
a4
3
7 = 3 + __
11 = 3 + __ + __
15 = 3 + __ + __ + __
5
a5
19 = 3 + __ + __ + __ + __
Arithmetic Sequences
To find the nth term of a sequence (an) where a1 is the first term in the sequence and d is the common difference:
an = a1 + (n ­ 1)d
2
Arithmetic Sequences
March 20, 2017
Arithmetic Sequences
Example 1:
an = a1 + (n ­ 1)d
Find the 15th term (a15) for the following arithmetic sequence: 5, 8, 11, 14, ...
Arithmetic Sequences
Example 2:
an = a1 + (n ­ 1)d
Find the 25th term (a25) for the arithmetic sequence in which a2 = 4 and a5 = 22:
3
Arithmetic Sequences
March 20, 2017
Arithmetic Sequences
Arithmetic Means: The terms between two given terms of an arithmetic sequence
10, 13, 16, 22
10, 14, 18, 22
10, 16, 22
Arithmetic Mean: A single mean between two numbers or the arithmetic average. For terms a & b the arithmetic mean is (a + b) / 2
10, 16, 22
Arithmetic Sequences
Example 3:
Find the arithmetic mean of 4 and 9.
4
Arithmetic Sequences
March 20, 2017
Arithmetic Sequences
Example 4:
an = a1 + (n ­ 1)d
Insert four arithmetic means between 15 & 50.
5