Question

What is the term to term rule for the sequence 4,12,36,108,324

Answer 1

seems to be a geometric sequence

each term is 3 times the previus

$a_n=a_1(r)^{n-1}$
$a_n$ is the nth term
$a_1$ is the first term
r is the comon ratio
n=which term


so first term is 4 and the common ratio is 3 so

$a_n=4(3)^{n-1}$

so the formula is
$a_n=4(3)^{n-1}$ or in other notation
$f(n)=4(3)^{n-1}$

Answer 2

The term to term rule for the sequence is a × 3ⁿ⁻¹.

This so a geometric progression. The formula will be arⁿ⁻¹

Here, the first term is 4, the common ratio is 12/4 = 3.

Therefore, the nth term will be:

= a × 3ⁿ⁻¹.

In conclusion, the term to term rule for the sequence is a × 3ⁿ⁻¹.

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