The first & the last term of an A.P are 17 & 350 respectively. If the C.d is 9 how many terms are there & what is their sum?

ML Aggarwal (avichal publication) Arithmetic Progression chapter 9, question no.5

Please a give a detailed of this question as it is very important for board examination

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=2n(a+l)

here n=38

S38=238[17+350]

=19×367

S38=6973