Q41 of 202 Page 9

In an A.P., the first term is 22, nth term is -11 and the sum to first n terms is 66. Find n and d, the common difference.

Given, First term, a = 22

nth term, an= -11 = l


and sum of n terms, Sn= 66


We know sum of n terms, Sn= [a + l]


66 = [22 – 11]


66 * 2 = n * 11


n = = 12


we know, an= a + (n – 1) d


-11 = 22 + (12 – 1) d


-11 – 22 = 11d


-33 = 11d


d = -3


Hence, number of terms, n = 12 and common difference, d = -3


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