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## Homework Statement

A finite arithmetic progression is given such that ##S_n>0## and ##d>0##. If the first member of the progression remains the same but ##d## increases by 2, then ##S_n## increases 3 times. If the first member of the progression remains the same but ##d## increases 4 times, then ##S_n## increases 5 times. Find ##d##.

## Homework Equations

##S_n=\frac{2a_1+d(n-1)}{2}\cdot n##

## The Attempt at a Solution

##\frac{2a_1+2d(n-1)}{2}\cdot n=\frac{2a_1+d(n-1)}{2}\cdot n \cdot 3##

##\frac{2a_1+4d(n-1)}{2}\cdot n=\frac{2a_1+d(n-1)}{2}\cdot n \cdot 5##

When I try to solve this I get ##a_1=0## which is clearly not possible. Can somebody explain me what am I doing wrong?

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