Question

The first term of a geometric sequence is 4 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?

Answer 1

first term`=a_1=4`, common ratio`=r=-2` and number of terms`=n=5`

Sum of geometric series up to `n` tems is given by

`S_n=(a_1(1-r^n))/(1-r)`

Where `S_n` is the sum to `n` terms, `n` is number of terms, `a_1` is the first term, `r` is the common ratio.

Here `a_1=4`, `n=5` and `r=-2`

`implies S_5=(4(1-(-2)^5))/(1-(-2))=(4(1-(-32)))/(1+2)=(4(1+32))/3=(4(33))/3=4*11=44`

Hence, the sum is `44`