Question

13) Algebraic expression of an arithmetic sequence is 5n+3. Find sum of first 39 terms?

Answer 1

$\huge \fcolorbox{red}{pink}{Solution :)}$

Given ,

• nth term of an AP is 5n + 3

Thus ,

First term = 5(1) + 3 = 5 +3 = 8

Second term = 5(2) + 3 = 10 + 3 = 13

It implies , the common difference is 5

We know that , the sum of first nth term of an AP is given by

$\large \mathtt{ \fbox{S = \frac{n}{2} (2a + (n - 1)d}}$

Substitute the known values , we get

$\sf \hookrightarrow S = \frac{39}{2} \bigg(2 \times 8 + (39 - 1)5 \bigg) \\ \\ \sf \hookrightarrow S = \frac{39}{2} \bigg(16 + (38)5 \bigg) \\ \\ \sf \hookrightarrow S = \frac{39}{2} (16 + 190) \\ \\ \sf \hookrightarrow S = \frac{39}{ \cancel{2}} ( \cancel{206}) \\ \\ \sf \hookrightarrow S = 39 \times 103 \\ \\ \sf \hookrightarrow S = 4017$

Hence , the sum of first 39 terms of an AP is 4017

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Answer 2

Answer:

I hope that helps you.always be happy .