Question

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Answer 1

First term, a = 7 

Last term, l = 49 

S_n = \(\frac{n}{2}\)[a + l] 

420 = \(\frac{n}{2}\)[7 + 49] 

840 = 56n 

n = 15 

Now, n = \(\frac{l - a}{d}\) + 1 

15 = \(\frac{49 + 7}{d}\) + 1 

15d = 42 + d

14d = 42 

d = 3 

Hence, it’s common difference is 3