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# Question 14. 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 that the first and the last terms of an A.P. are 17 and 350 respectively.

Also the common difference is 9,

Now we have to find out how many terms are there and what is their sum.
CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 14

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1. Given A.P. has first term(a) = 17,

Common difference(d) = 9 and last term(an) = 350.

We know nth term of an A.P. is given by, an = a + (n − 1)d.

=> 350 = 17 + (n − 1) 9

=> 350 = 17 + 9n − 9

=> 9n = 342

=> n = 38

Also we know sum of n terms of an A.P. is given by Sn = n[a + an]/2.

S38 = 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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