Question

# The sum of first n terms of an A.P. whose first terms 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 the common difference is 8. Find n.

Solution

## For $$1^{st}$$  AP$$a = 8, d= 20$$For $$2^{nd}$$ AP$$a' = -30 , d' = 8$$According to the question, $$S_n = S_{2n}'$$$$\Rightarrow \dfrac{n}{2}[2a+(n-1)d] = \dfrac{2n}{2}[2a' + (2n-1)d']$$$$\Rightarrow [2(8) + (n-1)20] = 2[2(-30)+(2n-1)8]$$$$\Rightarrow 2 \times 8 + n \times 20 - 20 = 2 [-60 + 16n -8]$$$$\Rightarrow 20 n - 4 = -136 + 32 n$$$$\Rightarrow -32 n+ 20 n = -136 + 4$$$$\Rightarrow n = 11$$Hence, the required value of n is 11.Maths

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