The first 31st term of a geometric sequence is 123 and the 32nd term is 1107. What is the 33rd term?

Feb 27, 2016

$9963$

Explanation:

We can find the common ratio of the geometric sequence by taking the ratio of any term with the preceding term.

So in this case we can say that the ratio $r = {T}_{32} / {T}_{31} = \frac{1107}{123} = 9$.

Consequently, the next term will be the previous term multiplied by the common ratio.

So in this case, ${T}_{33} = 9 \cdot {T}_{32}$

$= 9 \times 1107$

$= 9963$