Posted by **Miracle** on Tuesday, February 18, 2014 at 6:13am.

Find the sum of the nth terms of a G.P 5+15+45+...........What is the smallest number of the terms which will give a total of more than 10^8.

- Maths G.P. -
**Steve**, Tuesday, February 18, 2014 at 10:21am
a = 5

r = 3

Sn = a(1-r^n)/(1-r) = 5(3^n - 1)/2

So, we want

5(3^n-1)/2 > 10^8

3^n-1 > 4*10^7

3^n > 4*10^7 - 1

n > log(4*10^7 - 1)/log3

Now, using base 10 logs, and ignoring the useless -1,

n > (

n > 7+log4)/log3

n > 15.9

So the first 16 terms will sum to more than 10^8

As a sanity check, 5*3^15 = 7*10^7 so I figure just the last two or three terms will produce the desired amount, and the first 13 terms are just noise.

## Answer this Question

## Related Questions

- Maths - The nth term of a series is 2^n-1 +5n. Find the sum of the first n terms...
- Maths - Nth terms I have to find the first 5 terms in the nth sequence. please ...
- arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...
- arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...
- Math - 1)AP has U6=12.5 and U19=32 a+5d=12.5 (&) a+18d=32 (2) (2)-(1), d=1.5 ...
- Maths - Gemometric Progression - The sum of the first n terms of a series in n^3...
- Further mathematics - An exponential sequence (GP)of positive terms and a linear...
- Maths - Hi, I am working on some Nth problems - can anyone tell me if this is ...
- maths - the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and...
- maths - 1) The first term of arithmetic progression is -20 and the sum of it's ...