Good morning ☕️
Answer:
[tex]S=7((-\frac{2}{5})^{n-1} - 1)[/tex]
Step-by-step explanation:
Consider
(Vn) the geometric Sequence
S the sum
q the common ratio
V1 the first term
[tex]S=V_{1}\frac{1-q^{n-1} }{1-q}[/tex]
[tex]q=\frac{2}{-5}=-\frac{2}{5} \\ \\V_1=-5[/tex]
then
[tex]S=(-5)\frac{1-(-\frac{2}{5}) ^{n-1} }{1-(-\frac{2}{5} )}[/tex]
then (after a bit of calculations you’ll find)
[tex]S=7((-\frac{2}{5})^{n-1} - 1)[/tex]
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:)
