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# Question 36. The first and the last terms of an A.P. 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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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.

In this question we have been given that The first and the last terms of an A.P. are 17 and 350 respectively

It is also given that the common difference is 9,

Now we have to find how many terms are there and what is their sum.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 36

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1. Given A.P. has first term(a) = 17, common difference(d) = 9 and last term(an) = 350.

By using the formula of nth term of an A.P.

anÂ = a + (n â€“ 1)d

So,

=> 350 = 17 + (n â€“ 1) 9

=> 350 = 17 + 9n â€“ 9

=> 9n = 342

=> n = 38

By using the formula of the sum of first n terms of an A.P.

SnÂ = n[a + an] / 2.

S38Â = 38(17 + 350)/2

= 19(367) = 6973

Hence, the number of terms of the given A.P is 38 and sum is 6973.

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