Question

In an A.P. the first term is 2, and the sum of the first 5 terms is one-fourth of the next 5 terms. Show that 20th term is - 112

Answer 1

Given,

An AP whose first term is 2 

To find : 20^th term of an AP 

It is given that the sum of the first five terms is one-fourth of the next 5 terms 

So,

5a + 10d = \(\frac{1}{4}\)(5a + 35d)

20a + 40d = 5a + 35d 

15a + 5d = 0 

Substituting a as 2 we get,

d = - 6 

Hence,

20^th term is a + 19d = - 112