Question

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

Answer 1

Here, First term`(a_1) = 2`

If `S_5` is the sum of first five term and, `S_10` is the sum of first 10 terms, then, sum of 6 terms to 10 terms will be
`S_10-S_5`.
We are given,
`S_5 = 1/4(S_10-S_5)`
`=>5/4S_5 = 1/4S_10`
`=>5S_5 = S_10`
`=>5**(5/2(2a_1+4d)) = (10/2(2a_1+9d))`
`=>5a_1+10d = 2a_1+9d`
`=>d=-3a_1`
As `a_1 = 2`
`=> d = -6` Now, `a_20 = a_1+(20-1)*d`
`a_20 = 2+(20-1)**6=-112`