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The first and the last terms of an A.P. are 17 and 350 respect

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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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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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Text solutionVerified

From the question it is give that,

First term

a = 17

Last term

= 350

Common difference

d = 9

We know that,

T_{n} = a + (n - 1) d

350 = 17 + (n - 1) \times 9 350 - 17 = 9 n - 9 333 + 9 = 9 n 342 = 9 n n = 342/9

n = 38

S_{n} = (n /2) (2 a + (n - 1) d) S_{38} = (38/2) ((2 \times 17) + (38 - 1) d) = 19 (34 + (37 \times 9)) = 19 (34 + 333) = 19 \times 367 = 6973

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Question Text	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?
Answer Type	Text solution:1
Upvotes	150