Question

In an A.P. the first term is 8, n^th term is 33 and the sum of first n term is 123. Find n and the d, the common difference.

Answer 1

Given,

The first term of the A.P (a) = 8

The nth term of the A.P (l) = 33

And, the sum of all the terms S_n = 123

Let the common difference of the A.P. be d.

So, find the number of terms by

123 = (\(\frac{n}{2}\))(8 + 33)

123 = (\(\frac{n}{2}\))(41)

n = \(\frac{(123 \,\times\, 2)}{41}\)

n = \(\frac{246}{41}\)

n = 6

Next, to find the common difference of the A.P. we know that

l = a + (n – 1)d

33 = 8 + (6 – 1)d

33 = 8 + 5d

5d = 25

d = 5

Thus, the number of terms is n = 6 and the common difference of the A.P. is d = 5.