Question

The first term is $1$ in the geometric sequence $1,-3,9,-27,\dots$. What is the 7th term of the geometric sequence?

• A. $-243$
• B. $-30$
• C. $81$
• D. $189$
• E. $729$

Answer 1

The correct option is E $729$

A geometric sequence has a constant ratio (common ratio) between consecutive terms.

For the sequence $1,-3,9,-27,...$, the common ratio is $-3$ because:

$1(-3)=-3$ and $(-3)(-3)=9$

Since $1^{st}$ term is $1$, second is $-3$ and $4^{th}$ term is $-27$, then

$5^{th}$ term $=$ $(-27)(-3)=81$

$6^{th}$ term $=$ $\left(81\right)(-3)=-243$

$7^{th}$ term $=$ $(-243)(-3)=729$

Hence, option E is the correct answer.