# algebra

write an explicit formula for the nth term an for 17,20,23,26

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1. n = 1, a1 = 17 = 3 * 1 + 14 = 3 + 14

n = 2, a2 = 20 = 3 * 2 + 14 = 6 + 14

n = 3 , a3 = 23 = 3 * 3 + 14 = 9 + 14

n = 4 , a4 = 26 = 3 * 4 + 14 = 12 + 14

an = 3 n + 14

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2. OR

17, 20, 23, 26 is an arithmetic progression.

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:

an = a1 + ( n - 1 ) * d

In this case the initial term a1 = 17, the common difference d = 3

an = a1 + ( n - 1 ) * d

an = 17 + ( n - 1 ) * 3

an = 17 + 3 * n - 3 * 1 = 17 + 3 n - 3 = 14 + 3 n = 3 n + 14

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