Question

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

Answer 1

Yes, it is true.

Explanation:

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.