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? - Mathematics

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?

Given that,

a = 17

l = 350

d = 9

Let there be n terms in the A.P.

l = a + (n − 1) d

350 = 17 + (n − 1)9

333 = (n − 1)9

(n − 1) = 37

n = 38

`S_n = n/2(a+l)`

`=>S_n=38/2(17+350) = 19(367)= 6973`

Thus, this A.P. contains 38 terms and the sum of the terms of this A.P. is 6973.

Concept: Sum of First n Terms of an AP

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Chapter 5 Arithmetic Progressions
Exercise 5.3 | Q 6 | Page 113