SOLUTION: The first three terms of a geometric progression are x+1, x-3 and x-1. Find (i) the value of x, (ii) the first term, (iii) the sum to infinity.

Algebra ->  Sequences-and-series -> SOLUTION: The first three terms of a geometric progression are x+1, x-3 and x-1. Find (i) the value of x, (ii) the first term, (iii) the sum to infinity.      Log On


   

Question 1102001: The first three terms of a geometric progression are x+1, x-3 and x-1. Find
(i) the value of x,
(ii) the first term,
(iii) the sum to infinity.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find the successive ratios, which also will give the value for x in the process.
%28x-3%29%2F%28x%2B1%29=%28x-1%29%2F%28x-3%29

%28x-3%29%5E2=%28x%2B1%29%28x-1%29
x%5E2-6x%2B9=x%5E2-1
-6x%2B9=-1
6x-9=1
6x=10
x=10%2F6
highlight%28x=5%2F3%29-------value of x

First Term: x%2B1=5%2F3%2B1=5%2F3%2B3%2F3=highlight%288%2F3%29

Common Ratio: %28x-3%29%2Fx%2B1%29
%285%2F3-3%29%2F%288%2F3%29
%285%2F3-3%29%283%2F8%29
%285-9%29%2F8
-4%2F8
highlight%28r=-1%2F2%29


You may find a formula for sum to infinity if you look in https://en.wikipedia.org/wiki/Geometric_series, or in your textbook.