Question

the 10th term of an ap is -7 and the sum of first 6 terms minus 27 find the sum of first 8 terms​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The sum of first 8 terms is $\frac{-508}{13}$

Step-by-step explanation:

Formula of nth term of AP = $a_n=a+(n-1)d$ ---1

Formula of sum of first n terms = $S_n=\frac{n}{2}(2a+(n-1)d)$ ---2

Substitute n = 10 in 1

$a_{10}=a+(10-1)d$

We are given that the 10th term of an ap is -7

So,$a+9d=-7$ ----- A

Substitute n = 6 in 2

$S_{6}=\frac{6}{2}(2a+(6-1)d)$

We are given that The sum of first 6 terms is -27

$3(2a+5d)=-27$ ---B

Substitute the value of a from A in B

$3(2(-7-9d)+5d)=-27\\3(-14-18d+5d)=-27\\-14-13d=-9\\-13d=5\\d=\frac{-5}{13}$

Substitute the value of d in A

$a+9(\frac{-5}{13})=-7\\a=-7+\frac{45}{13}\\a=\frac{-46}{13}$

Substitute n = 8 in 2

$s_8=\frac{8}{2}(2(\frac{-46}{13})+(8-1)(\frac{-5}{13}))=\frac{-508}{13}$

Hence The sum of first 8 terms is $\frac{-508}{13}$

#Learn more:

The sum of first 7 terms of ap is 63 and sum of next 7 terms is 161 find 28th term of ap

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