This is the basic question from arithmetic progression chapter in which we have to find the sum and the no of terms of an AP, if the first and last term of an AP are 17 and 350 respectively and their common difference is 9.

Book RS Aggarwal, Class 10, chapter 5C, question no 23.

Let a and d are first term and common difference for an AP.

Number of terms of AP is n

Last term =nth term =l=an

We have a=17,d=9,l=350

We know a+(n−1)d=350

⇒17+(n−1)9=350

⇒(n−1)9=350−17

⇒(n−1)9=333

⇒n−1=333/9

⇒n−1=37

⇒n=37+1

∴n=38

Therefore, number of terms in given AP is n=38

Sum of n terms of AP is Sn

Sn=n/2(a+l)

here n=38

S38=38/2[17+350]

=19×367

S38=6973