Posted by Byun on Tuesday, December 20, 2011 at 12:45am.
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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