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Question

# The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, then find the number of terms in the AP and their sum.

A

32; 6973

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B

38; 6973

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C

32; 7114

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D

38; 7114

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Solution

## The correct option is B 38; 6973 Given, First term =a=17 Last term =l=350 Common difference =d=9 Using formula an=a+(n−1)d, we can say that 350=17+(n−1)(9) ⇒350=17+9n−9 ⇒342=9n ⇒n=3429=38 Applying formula, Sn=n2(2a+(n−1)d), we get S38=382(34+(38−1)9) ⇒S38=19(34+333)=6973 Therefore, there are 38 terms and their sum is equal to 6973.

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