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

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

Answers (1)

Let 55 is the nth term of an AP 

\therefore a\textsubscript{n} = 55 $ \ldots $ (1)\\

 Given AP is 7, 10, 13........

 Here a = 7, d = 10 - 7

    d = 3

 By equation (1) is a\textsubscript{n} = 55\\ 

\\a + (n - 1) \times d = 55 $ \ldots $ (2) (using a\textsubscript{n} = a + (n-1)d)\\ 7 + (n - 1) \times 3 = 55\\ (n - 1) \times 3 = 55 - 7\\ (n - 1) \times 3 = 48\\ n - 1 = \frac{48}{3} \\ n - 1 = 16\\ n = 17\\

Here n is a positive integer.

Hence 55 is 17th term of an AP

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