Question

What is the seventh term of the geometric sequence with a first term of 729 and a common ratio of ?

Answer 1

Given:

Given that the first term of the geometric sequence is 729.

The common ratio is $\frac{1}{3}$

We need to determine the seventh term of the sequence.

Seventh term:

The seventh term of the sequence can be determined using the formula,

$a_n=a_1(r)^{n-1}$

To find the seventh term, let us substitute n = 7 in the above formula, we get;

$a_7=a_1(r)^{6}$

Now, substituting $a_1= 729$ and $r=\frac{1}{3}$, we get;

$a_7=729(\frac{1}{3})^{6}$

$a_7=729(\frac{1}{729})$

$a_7=1$

Thus, the seventh term of the geometric sequence is 1.