Question

What is the sum of the geometric sequence 1, -4, 16, if there are 7 terms? (1 points)

-5,461

5,461

-3,277

3,277

Answer 1

can you tell me what the common ratio r is...?

Answer 2

Huh ?

Answer 3

well a geometric sequence needs a common ratio

the next term = current term x the common ratio....

so what did you multiply the 1st term by to get the 2nd term...

does it work when you multiply the 2nd term by the same value to get the 3rd term

Answer 4

You multiply -4 To get the next term

Answer 5

@campbell_st

Answer 6

great thats the common ratio

r = -4

and the 1st term is a = 1

then you need to find the sum of 7 terms so n = 7

and use the formula

\[S_{n} = \frac{1 \times (1 - r^n)}{1 - r} \]

make the necessary substitutions and you'll get the sum of 7 terms

Answer 7

What ?

Answer 8

Like the gent said, plug in the values of \(r, n\) to find \(S_n\) which is the sum of the first \(n\) terms of the geometric sequence with \(r = -4\) and \(a=1\).

\[S_7 = \frac{1*(1-(-4)^7)}{1-(-4)} = \]

You can check your work by finding the first 7 terms and adding them up.