Question

What is the sum of the geometric sequence 1, -4, 16, ... if there are 7 terms?
Choose one answer.
a. -5,461
b. 5,461
c. -3,277
d. 3,277

Answer 1

Someone please helP!

Answer 2

The first term is 1. So a = 1

The common ratio is -4. So r = -4


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Plug these values into the formula Sn = a*(1-r^n)/(1-r) to compute the nth partial sum


Sn = a*(1-r^n)/(1-r)

Sn = 1*(1-(-4)^n)/(1-(-4))

Sn = 1*(1-(-4)^n)/5

S7 = 1*(1-(-4)^7)/5

S7 = 1*(1-(-16384))/5

S7 = 1*(1+16384)/5

S7 = 3227

So the 7th partial sum if 3227, which means that the sum of the first seven terms is 3227

Answer 3

oops meant to write 3277 and not 3227...

Answer 4

but hopefully you get the idea