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If S7=49 and S17=289 then find …

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If S7=49 and S17=289 then find Sum of n terms.

Posted by Saket S 6 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 3 months ago

Formula of first n terms in AP = {tex}S_n = \frac{n}{2}(2a+(n-1)d){/tex}

Substitute n = 7

So,{tex} S_7 = \frac{7}{2}(2a+6d){/tex}

{tex}49 = \frac{7}{2}(2a+6d){/tex}

{tex}49 \times \frac{2}{7} = 2a+6d{/tex}

14= 2a+6d

Substitute n = 17

{tex}S_{17} = \frac{17}{2}(2a+16d){/tex}

{tex}289 = \frac{17}{2}(2a+16d){/tex}

{tex}289 \times \frac{2}{17} = 2a+16d{/tex}

34= 2a+16d

34= 2a+10d+6d

Using A

34= 14+10d

20 = 10d

d=2

Substitute the value of d in A

14= 2a+12

2= 2a

a=1

So, {tex} S_n = \frac{n}{2}(2(1)+(n-1)2){/tex}

{tex}S_n = \frac{n}{2}(2+(n-1)2){/tex}

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CBSE > Class 10 > Mathematics