Question

Part A What is the explicit formula the sequence 8,10,12.5,15.625...?

Answer 1

Given:

The sequence is 8, 10, 12.5, 15.625,...

To find:

The explicit formula for the given sequence.

Solution:

We have,

8, 10, 12.5, 15.625,...

Here, the first terms is 8.

$\dfrac{10}{8}=1.25$

$\dfrac{12.5}{10}=1.25$

$\dfrac{15.625}{12.5}=1.25$

The common ratio is 1.25. So, the given sequence is a geometric sequence.

The explicit formula for a geometric sequence is:

$a_n=ar^{n-1}$

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

The explicit formula for the given geometric sequence is:

$a_n=8(1.25)^{n-1}$

Therefore, the correct option is A.