What is the formula to increase x by y z times?
For example the number 4 I want to increase by 4 50 times. I added it out (4+8+12+16+20+24 etc....to 204) and got the right answer 5304 but what is the algebraic formula to get it vs adding them out?
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1$\begingroup$ Welcome to Mathematics Stack Exchange. This is an arithmetic series. The sum is $\dfrac{51(4+204)}2$ $\endgroup$– J. W. TannerCommented Jan 11 at 4:44
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$\begingroup$ This kind of question has been asked and answered many times on this site. Please use the search engine. $\endgroup$– Anne BauvalCommented Jan 11 at 6:29
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1 Answer
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What is the formula to increase $x$ by $y$, $z$ times?
According to your e.g. you want to find, $$S:{=x+(x+y)+(x+2y)+...+(x+zy)\\=(z+1)x+y(1+2+3+...+z)\\ =(z+1)x+y\cdot\frac{z(z+1)}{2}\quad(\text{Sum of first $z$ integers.})\\=(z+1)\left(x+\frac{yz}2\right)}$$
Now, put $x=4,y=4,z=50$ and check it, $$(50+1)\cdot\left(4+\frac{4\times50}{2}\right)=5304$$
