What is the common ratio for the geometric sequence? 43,4,12,36,...

ANSWER

The common ratio is
[tex]3[/tex]

EXPLANATION

The given sequence is
[tex] \frac{4}{3} ,4,12,36,...[/tex]

To find the common ratio of the geometric sequence, we need to express the subsequent terms over the previous terms and simplify.

If the result is the same then the resulting value is the common ratio.

Let us express the second term over the first term to obtain,

[tex] \frac{4}{ \frac{4}{3} } = 4 \div \frac{4}{3} = 4 \times \frac{3}{4} = 3[/tex]

The third term over the second term will also give,

[tex] \frac{12}{4} = 3[/tex]

The fourth term over the third term will give,

[tex] \frac{36}{12} = 3[/tex]

Therefore the common ratio is,

[tex]3[/tex]