Question

Write the explicit formula for the geometric sequence. Then find the fifth term in the sequence.

\(a_1 = –4,~a_2 = 8,~a_3 = –16\)

A) \(a_n = –4 · (2)^n; –64\)
B) \(a_n = –4 · (–2)^{n–1}; –64\)
C) \(a_n = –4 · (–2)^n; 128\)
D) \(a_n = –2 · (–4)^{n–1}; –512\)

Answer 1

well the general term in a geometric sequence is

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

you know the 1st term.... you need to common ratio r..... before you can find the 5th term

hope it helps

Answer 2

Using what you said would B be correct?
\(a_{n} =a_{1} \times r^{n -1}\)
\(a_{n} =-4 \times -2^{n -1}\)

Answer 3

yeap...thats it, you now just need to substitute n = 5 and then evaluate