1. ## Determine a

Determine a when : a+a*1.2+a*(1.2)^2+a*(1.2)^2+a*(1.2)^3+...+a*(1.2)^ 24=2000
It's under mixed exercises in my book. But i can't find anything that looks like this in my book. I just can't find out what to do, so ended up trying to guess a and slove it. Anyone can give me a hint. I know it's probarbly very easy...

2. ## Re: Determine a

Originally Posted by Portion
Determine a when : a+a*1.2+a*(1.2)^2+a*(1.2)^2+a*(1.2)^3+...+a*(1.2)^ 24=2000
It's under mixed exercises in my book. But i can't find anything that looks like this in my book. I just can't find out what to do, so ended up trying to guess a and slove it. Anyone can give me a hint. I know it's probarbly very easy...
Sum of a geometrical progression.

Call the sum S, then multiply it by 1.2, then do 1.2 S - S and see what you get after simplifying.

3. ## Re: Determine a

Hello, Portion!

$\text{Determine }a\text{ when:}$

. . $a+a(1.2)+a(1.2)^2+a(1.2)^2+a(1.2)^3+ \hdots +a(1.2)^{24} \:=\:2000$

Matt Westwood identitied the equation: the sum of a geometric sequence.

The first term is: $a.$
The common ratio is: $r = 1.2$
And there are: $n = 25$ terms.

The sum of the first $n$ terms of a geometric sequence

. . is given by: . $S_n \;=\;a\,\frac{r^n-1}{r-1}$

So we have: . $a\,\frac{1.2^{25} - 1}{1.2-1} \:=\:2000$

. . Solve for $a.$

4. ## Re: Determine a

a=2000*(1.2-1) / (1.2^25) -1 = 4.237457964
ans * (1.2^25)-1 / 1.2-1 = 2000 ))) So happy now Thx!

5. ## Re: Determine a

Well yes okay, but my technique doesn't require you to learn a formula to plug numbers into, it teaches you why the formula works. Still, if it's just a formula for doing your maths homework you want, rather than understanding of why, then no worries.