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.

Question

Philoid · Accepted Answer

Given, First term, a = 8

N^th term, a_n = 33 = l

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

123 = [8 + 33]

123 * 2 = n * 41

n = = = 6

We know,

a_n= 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