Question

Sum of the first 20 terms of an AP is −240, and its first term is 7. Find its 24^th term ?

Answer 1

First term of the A.P. (a) = 7; sum of first 20 terms = −240.

The sum of first n terms of an AP,`S_n= n/2[2a+(n-1)d]`, where a is the first term and d is the common difference.

`therefore S_n=20/2[2xx7+(20-1)d]=240`

`rArr10[14+19d]=-240`

`rArr14+19d=-24`

`rArr19d=-38`

`rArrd=-2`

Now, 24^th term of the AP, `a_24=a+(24-1)d`

On putting respective values of a and d, we get

a₂₄ + 7 + 23 × (− 2) = 7 − 46 = − 39

Hence, 24^th term of the given AP is −39.