Math
posted by Byun .
In an arithmetic sequence, the first term is 5, and the fifth term is 21. What is the second term? Help please ASAP!!

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:
an = a1 + ( n  1 ) * d
In this case:
a1 = 5
n = 5
a5 = 21
an = a1 + ( n  1 ) * d
a5 = a1 + ( 5  1 ) * d
21 = 5 + 4 * d
21  5 = 4 d
16 = 4 d Divide both sides with 4
16 / 4 = 4 d / 4
4 = d
d = 4
a2 = a1 + d
a2 = 5 + 4
a2 = 9 
The increase per term is (21  5)/(5  1)
= 16/4 = 4
Add 4 to the first term to get the second term
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