Q10 of 89 Page 51

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

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


an = 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 17th term of given AP


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