Question

# The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is $-30$ and common difference is 8 . Find n.

Solution

## According to the question, we have $\frac{n}{2}\left[2\left(8\right)+\left(n-1\right)20\right]=\frac{2n}{2}\left[2\left(-30\right)+\left(2n-1\right)8\right]\phantom{\rule{0ex}{0ex}}⇒\left[16+20n-20\right]=2\left[-60+16n-8\right]\phantom{\rule{0ex}{0ex}}⇒20n-4=-136+32n\phantom{\rule{0ex}{0ex}}⇒12n=132\phantom{\rule{0ex}{0ex}}⇒n=11$MathematicsRD Sharma (2016)Standard X

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