Question

An

a.P. Consists of 43 terms, if the sum of five middle most terms is 195, then the sum of the

a.P.

Answer 1

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Answer 2

The sum of 43 terms of AP is 1677

Explanation:

There are total 43 terms.

Let first term be A and common difference d

Middle most five term:-

First 19 term---Middle five term-----Last 19 term

So, Most middle fiver terms are, $a_{20},a_{21},a_{22},a_{23},a_{24}$

Let $a_{22}=a$  and common difference is d

$a_{20}=a-2d$

$a_{21}=a-d$

$a_{23}=a+d$

$a_{24}=a+2d$

Sum of these five term is 195

a - 2d + a-d + a + a + d + a + 2d = 195

                                               5a = 195

                                                 a = 39

So, 22th term of AP is 39

i,e $A+21d = 39$

Sum of 43 term of AP:

$S_n=\dfrac{n}{2}(2A+(n-1)d)$

$S_{43}=\dfrac{43}{2}(2A+42d)$

$S_{43}=\dfrac{43}{2}\times 2(A+21d)$

$S_{43}=43\times 39$

$S_{43}=1677$

hence, the sum of 43 terms of AP is 1677

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Sum of nth term of AP

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