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.

Explanation

Let the first term, common difference and the number of terms of an AP are a, d and n respectively.
Given that, first term (a) = - 5 and last term `(l)` = 45
Sum of the terms of the AP `= 120impliesS_(n)=120`
We know that, if last term of an AP is known, jthen sum of `n` terms of an AP is,
` " " S_(n)=(n)/(2)(a+l)`
`implies 120 =(n)/(2)(-5+45)implies12xx2=40xxn`
`implies n=3xx2impliesn=6`
` :.` Number of terms of an AP is known, then teh `n`th term of an AP is,
` l =a+(n-1)dimplies45= -5+(6-1)d`
`implies 50=5dimpliesd=10`
So, the common difference is 10.
Hence, number of terms and the common difference of an AP are 6 and 10 respectively.