Q.The first and the last term of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there and what is their sum?
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Let a and d are first term and common difference for an AP.
Number of terms of AP is n
Last term =n
th
term =l=a
n
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 S
n
S
n
=
2
n
(a+l)
here n=38
S
38
=
2
38
[17+350]
=19×367
S
38
=6973
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