Find whether 55 is a term of the AP, 7, 10, 13, … or not. If yes, find which term it is.

Question

Philoid · Accepted Answer

let the first term, common difference of an AP are a and d respectively.

a = 7

d = a₂ - a₁ = 10 - 7 = 3

Let the nth term of this AP is 55

Then

a_n = 55

a + (n - 1)d = 55

7 + (n - 1)3 = 55

3(n - 1) = 48

n - 1 = 16

n = 17

so the 55 is a term of given AP

and 55 is the 17^th term of given AP