Question

The first term of an AP is -5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Answer 1

Here a=-5, l=45
Let the common difference and number of terms of A.P. be d and n respectively.
`:. S_(n)=(n)/(2)(a+l)`
`rArr 120=(n)/(2)(-5+45)`
`rArr n=6`
and `l=a+(n-1)d`
`45=-5+(6-1)d`
`rArr 50=5d`
`rArr d=10`