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A four-term sequence has its first three terms in geometric progression and its last three terms in arithmetic progression with common difference 6. If the first term and the fourth term are equal, what is the value of the fourth term?

1. 16
2. 8
3. 4
4. 2

Correct answer: 8

Solution

The first three terms being in geometric progression means that the ratio between consecutive terms is constant, while the last three terms being in arithmetic progression with a common difference of 6 indicates that the difference between consecutive terms is fixed. Given that the first and fourth terms are equal, we can set up equations based on these properties and solve for the terms, ultimately finding that the fourth term is 8.

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