Question

The sum of the first n terms of the geometric sequence
-1, -3, -9,... is -3280. Find the value of n. Express answer in simplest fractional form.
1. t1= -1
2. r = 3
3. S6 = I got -364 but it's not the right answer
4. n = I keep getting a decimal number: 18.72075441...

Answer 1

a = -1
r = 3
Sn = (-1)(3^n-1)/(3-1)
= (1-3^n)/2 = -3280
1-3^n = -6560
3^n = 6561
n = 8

Answer 2

Just use the sum formula

for a GP
sum(n) = a(r^n - 1)/(r-1)

for ours: a = -1, r = 3

-1( 3^n - 1)/(3-1) = -3280
3^n - 1 = 6560
3^n = 6561

you could just play around with powers of 3
or you could use logs

n log3 = log 6561
n = log6561/log3 = 8

check:
sum(8) = -1(3^8 - 1)/(3-1)
= -1( 6561 - 1)/2
= -3280