Write the explicit formula for the sequence below and use it to find the 16th term: 6, -24, 96, -384, . . .

Given:

The sequence is:

To find:

The explicit formula for the given sequence and then find the 16th term.

Solution:

We have,

The ratio between two consecutive terms are:

The given sequence has a common ratio. So, the given sequence is a geometric sequence with first term 6 and common ratio .

The explicit formula of a geometric sequence is:

Where, a is the first term and r is the common ratio.

Putting in the above formula, we get

We need to find the 16th term. So, put in the above formula.

Therefore, the explicit formula for the given sequence is   and 16th term of the given sequence is .

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