Q40 of 202 Page 9

In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

Given, First term, a = 8

Nth term, an = 33 = l


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


123 = [8 + 33]


123 * 2 = n * 41


n = = = 6


We know,


an= a + (n – 1) d


33 = 8 + (6 – 1) d


33 – 8 = 5d


25 = 5d


d = 5


Hence, number of terms n = 6 and common difference, d = 5


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