Answer:
40
Step-by-step explanation:
we need the sum of the first 4 terms of this GS
= (-2)(-3)^0 + (-2)(-3)^(2-1) + (-2)(-3)^(3-1) + (-2)(-3)^(4-1)
= -2( 1 + -3 + 9 + -27)
= 2 * -20
= 40
Answer:
Sum of series is 40.
Step-by-step explanation:
Given : Geometric series .
To find : Sum of geometric series.
Solution : We have given that ∑[tex](-2)(-3)^{n-1}[/tex] n = 1 to 4
For n = 1
[tex]S_{1}[/tex] = [tex](-2)(-3)^{1-1}[/tex]
[tex]S_{1}[/tex] = (-2)(1)
[tex]S_{1}[/tex] = -2.
For n =2
[tex]S_{2}[/tex] = [tex](-2)(-3)^{2-1}[/tex].
[tex]S_{2}[/tex] = 6.
For n =3
[tex]S_{3}[/tex] = [tex](-2)(-3)^{3-1}[/tex].
[tex]S_{3}[/tex] = [tex](-2)(-3)^{2}[/tex].
[tex]S_{3}[/tex] = (-2)(9).
[tex]S_{3}[/tex] = -1.
For n =4
[tex]S_{4}[/tex] = [tex](-2)(-3)^{4-1}[/tex].
[tex]S_{4}[/tex] = [tex](-2)(-3)^{3}[/tex].
[tex]S_{4}[/tex] = [tex](-2)(-27)[/tex].
[tex]S_{4}[/tex] = 54.
Sum of all
[tex]S_{1}[/tex] + [tex]S_{2}[/tex] + [tex]S_{3}[/tex] + [tex]S_{4}[/tex].
-2 + 6 + (-18) + 54
-2 +6 -18 +54
4 -18+54
-14+54
40.
Therefore, Sum of series is 40.
