Progression

Quote:

Originally Posted by princess_anna57

The seventh term of a geometric progression is 0.775 and the ninth term is 0.995.
(a) Find the common ratio (to 3 decimal places).
(b) List the first three terms of the geometric progression (to 6 decimal places).
(c) Find the sum of the first ten terms (to 3 decimal places).

recall that the terms of a geometric progression are given by

$a_n = ar^{n - 1}$ for $n = 1,~2,~3, \dots$

where $a_n$ is the $n$ th term, $a$ is the first term, $r = \frac {a_2}{a_1} = \frac {a_3}{a_2} = \cdots$ is the common ratio.

thus, we have the 7th term is $ar^6 = 0.775$ and the 9th term is $ar^8 = 0.995$

so, $\frac {ar^8}{ar^6} = \frac {0.995}{0.775}$

you can use that to find $r$ , once you have $r$ you can find $a$ . once you have $a$ and $r$ , you can answer all the questions

good luck

EDIT: also, recall that the sum $S_n$ of the first n terms is given by $S_n = a \cdot \frac {1 - r^n}{1 - r}$