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