The sum using summation notation will be - 312. The sum of the following progression is found by the formula as [tex]S_n = \frac{a(1 - r^n)}{(1 - r)}[/tex].
Geometric Progression (G.P.) is a sort of sequence in which each successive phrase is obtained by multiplying the prior term by a set number known as a common ratio.
This progression is also known as a pattern-following geometric sequence of integers. Here you may also learn about mathematical progression.
A non-zero value is obtained by multiplying the common ratio by each phrase to obtain the next term 5 - 15 45 - 135.. is an example of a geometric series with a common ratio of -3.
The common ratio will be;
[tex]\rm r= \frac{-15}{3} \\\\ \rm r= -5[/tex]
The first term is 3
So the sum using summation notation will be;
[tex]S_n = \frac{a(1 - r^n)}{(1 - r)} \\\\ S_n = \frac{3(1 - (-5)^4)}{(1 - (-5))} \\\\ S_n =- 312[/tex]
Hence the sum using summation notation will be - 312.
To learn more about the geometric progression refer to;
https://brainly.com/question/14320920
