An important question has been from from ML Aggarwal book from Arithmetic Progression chapter 9. It is given that the first term of an AP is 5, the last term is 45 and the sum is 400. Calculate the number of terms and the common difference.

ML Aggarwal Avichal Publication

Arithmetic Progression chapter 9 question no 4

## first termÂ a=5, last termÂ l=45Â andÂ Snâ€‹Â = 400

Since,Â Snâ€‹=2nâ€‹(a+l)

â‡’400=2nâ€‹(5+45)

â‡’400=2nâ€‹(50)

â‡’400=n(25)

â‡’n=16

Since,Â l=a+(nâˆ’1)d

â‡’45=5+(16âˆ’1)d

â‡’45âˆ’5=(15)d

â‡’40=15d

â‡’d=1540â€‹

â‡’d=38â€‹