Question

Use the drop-downs to complete the sentences about this geometric sequence. 24, 12, 6, 3, … The common ratio is . The fifth term is .

Answer 1

A sequence is geometric if every two consecutive elements are in the same proportion. So, you start from a fixed element, and generate every next element by multiplying the previous one by the common ratio.

In this sequence, the first element is 24. Evert next element is half of its previous one, so the common ratio is 1/2. In fact, you generate the second term (12) by multiplying the first one (24) by 1/2.

Then, you generate the third element (6) by multiplying the second element (12) by 1/2.

Then, you generate the fourth element (3) by multiplying the third term (6) by 1/2.

So, it should be clear that you generate the fifth element by multiplying the fourth by 1/2. The fifth element is thus

`3 \cdot (1)/(2) = (3)/(2) = 1.5`

Answer 2

The common ratio is: 1/2

The fifth term is: 3/2

Explanation:

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