Question

The first and the last terms of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

Answer 1

First term, a = 5 

Last term, l = 45 

S_n = 400 

\(\frac{n}{2}\)[a + l] = 400

n[5 + 45] = 800

n = 16 

Now, n = \(\frac{l - a} {d}\) + 1

16 =\(\frac{45-5}{d}\) + 1 

16d = 40 + d 

15d = 40 

d =\(\frac{8}{3}\)

Hence, the common difference is \(\frac{8}{3}\)