Is the statement true or false: doubling each term in an arithmetic series will double the sum?

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Answer 1 · 2017-08-01T07:03:36

Yes, it is true.

Let the $n$ terms of the arithmetic series be

$a,a+d,a+2d,a+3d,..................a+(n-1)d$

Then $S_n=a+(a+d)+(a+2d)+(a+3d)+..................+a+(n-1)d$

Doubling each term on right hand side will make it

$2a+2(a+d)+2(a+2d)+2(a+3d)+..................+2(a+(n-1)d)$

= $2(a+(a+d)+(a+2d)+(a+3d)+..................+a+(n-1)d)$

= $2S_n$

Hence the sum too will be doubled.