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What is the sum of the first seven terms of the geometric series 2 − 8 + 32 − . . . ?

Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.

S7 = 6,554
S7 = −8,192
S7 = 8,192
S7 = 10,922

Respuesta :

kudzordzifrancis

Answer:

[tex]S_7=6554[/tex]

Step-by-step explanation:

The given series is [tex]2-8+32-...[/tex]

The first term of the sequence is

[tex]a_1=2[/tex]

There is a common ratio of

[tex]r=-4[/tex]

The sum of the first n terms of a geometric sequence is given by the formula;

[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]

We want to find the first seven terms so [tex]n=7[/tex]

We substitute the given values into the formula to obtain;

[tex]S_7=\frac{2(1-(-4)^7)}{1--4}[/tex]

[tex]S_7=\frac{2(1--16384)}{1--4}[/tex]

[tex]S_7=\frac{2(16385)}{5}[/tex]

[tex]S_7=2(3277)[/tex]

[tex]S_7=6554[/tex]

The correct answer is A