Question

HELP PLEASE!!!
What is the 7th term of the geometric sequence where a1 = -3 and a5 = -768?

14. What is the 7th term of the geometric sequence where a1 = -4,096 and a4 = 64?



15. What is the sum of the geometric sequence -3, 21, -147, ... if there are 6 terms?

Answer 1

well a term in a geometric sqeuence ios

\[a_{n} = a_{1} \times r^{n - 1}\]

you need to find the common ratio

so

\[-768 = -3 \times r^{5 -1}...or..... -768 = -3 \times r^4\]

solve for r

then the sum is

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

you ahve a1, you found r and know n = 7

just substitute to fine the sum

similar for the other questions, find the common ratio r 1st