Answer:
As we can see -15 = 5 * (-3); 45 = - 15 * (-3) and so on. This means that a_n = -3 * a_(n-1). The first term in our series is 5 so we obtain
5 - 15 + 45 - 135 + ... = summation from n equals zero to infinity of 5 * (-3)^n.
The sum using summation notation, assuming the suggested pattern continues is S = 1.25[1+[tex](-3)^{n}[/tex]].
A geometric progression is a sequence in which any element after the first is obtained by multiplying the previous element by a constant which is called a common ratio denoted by r.
For example, the sequence 1, 4, 16, 64,… is a geometric sequence with a common ratio of r = 4.
Given series is 5 - 15 + 45 - 135 + ...
Here the common ratio is -3 as you can see -15/5 = -3.
so using the below formula of the gp summation.
[tex]\sum\limits_{k = 1}^\infty {ar^{k - 1} = \frac{a}{{1 - r}}}[/tex]
Now our n is act like k so by putting value we get
S = 1.25[1+[tex](-3)^{n}[/tex]] which is the summation of the given gp.
Hence the given formula will be our summation.
For more information about the geometrical progression
https://brainly.com/question/4853032
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