Find the sum of the following arithmetic progressions- x-y x-y - 3x-2y x-y - 5x-3y x-y - to n terms

Sum of n terms = n/2(2a+(n 1)d) here a= x y/x=y #160; #160; #160; #160; d= (3x 2y/x+y) (x y/x+y) #160; #160; #160; #160; ...

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Byju's Answer

Standard X

Mathematics

Sum of N Terms of an AP

Find the sum ...

Question

Find the sum of the following arithmetic progressions:
$\frac{x - y}{x + y}, \frac{3 x - 2 y}{x + y}, \frac{5 x - 3 y}{x + y}, . . . .$ to $n$ terms

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Solution

sum of n terms = $n / 2 (2 a + (n - 1) d)$
here a= $x - y / x = y$
d= $(3 x - 2 y / x + y) - (x - y / x + y)$
= $2 x - y / x + y$

hence sum= $\frac{n}{2 (x + y)} {n (2 x - y) - y}$

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