# Given a geometric sequence with a1 = 6 and r = 2/3, write an explicit formula for An, the nth term of the sequence.

## a r(n-1)

An = 6 (2/3)^(n-1)

## If a1=-6 and r=−

1

3what will be the second term of the sequence?

## The explicit formula for the nth term (An) of a geometric sequence is given by:

An = a1 * r^(n-1)

Given that a1 = 6 and r = 2/3, we can substitute the values into the formula to find the explicit formula for An:

An = 6 * (2/3)^(n-1)

Therefore, the explicit formula for the nth term of the given geometric sequence is An = 6 * (2/3)^(n-1).

## To write an explicit formula for the nth term of a geometric sequence, we can use the formula:

An = a1 * r^(n-1)

Where:

- An represents the nth term of the sequence

- a1 is the first term of the sequence

- r is the common ratio of the sequence

- n represents the position of the term we want to find

In this case, you have been given a1 = 6 and r = 2/3. Plugging these values into the formula, we get:

An = 6 * (2/3)^(n-1)

Thus, the explicit formula for the nth term of the given geometric sequence is An = 6 * (2/3)^(n-1).