If the nth terms of the two AP’s 9, 7, 5, … and 24, 21, 18 … are the same, then find the value of n. Also, that term.


First term of first AP, a = 9


First term of second AP, A = 24


Common difference of first AP, d = 7 - 9 = - 2


Common difference of second AP, D = 21 - 24 = - 3


Given that nth term is same i.e


An = an


As we know, nth term of an AP is


an = a + (n - 1)d


where a = first term


an is nth term


d is the common difference


A + (n - 1)D = a + (n - 1)d


24 + (n - 1) (- 3) = 9 + (n - 1) (- 2)


24 - 3n + 3 = 9 - 2n + 2


27 - 3n = 11 - 2n


3n - 2n = 27 - 11


n = 16


i.e their 16th term is equal in both cases,


and a16 = A16 = a + 15d = 9 + 15 (- 2) = - 21


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