The sum of an infinite GP is 15. The sum of the squares of the terms is 45. Find the first term
@iambatman

Question

The sum of an infinite GP is 15. The sum of the squares of the terms is 45. Find the first term
@iambatman

anonymous · Answer

crashonce · Answer

no solution probided

dan815 · Answer

well write it out

dan815 · Answer

u have 2 eqn and 2 unknowns

anonymous · Answer

$$\sum_{n=0}^{\infty} ax^n = \frac{ a }{ 1-x }$$ set this equal to 15 find the pattern set the second equation = 45 and go from there.

anonymous · Answer

I suppose you'd start with:$$
15 = \sum_{k=1}^{\infty}ar^{k-1}=\frac{a}{1-r}
$$

crashonce · Answer

what about the squared part not sure about that

anonymous · Answer

$$\frac{ a^2 }{ 1-x^2 } = 45$$ do you mean this?

anonymous · Answer

If you squared the terms, you'd get $$
45 =\sum_{k=0}^{\infty }( ar^{k-1} )^2 =\sum_{k=0}^{\infty }a^2(r^2)^{k-1}  = \frac{a^2}{1-r^2}
$$

anonymous · Answer

I'll let wio handle this :D

dan815 · Answer

xD it was solved at 2 eqn and 2 unknown

anonymous · Answer

$$
45 = \frac{a}{1+r}\cdot \frac{a}{1-r} =  \frac{a}{1+r}\cdot 15
$$

crashonce · Answer

oooooooo right

anonymous · Answer

Hahaha.

crashonce · Answer

can u solve the rest for me @wio

anonymous · Answer

I probably could.

anonymous · Answer

First think you want to do is isolate the $r$ so you can sub it into the other formula.

crashonce · Answer

solve it please

anonymous · Answer

Why don't you finish it off, what is r?

anonymous · Answer

I meant to use r instead of x..

crashonce · Answer

(15-a)/15

anonymous · Answer

I don't know what that means

crashonce · Answer

$$\frac{ 15-a }{ 15 }$$

anonymous · Answer

I'm not sure what you mean, I got r = 2/3?

crashonce · Answer

dw i meant at first, not when solved

anonymous · Answer

Well you have r now lol, and a should be obvious so you can get the first term now :).

crashonce · Answer

5 lol

anonymous · Answer

Yeah :D