# Arithmetic and Geometric

Pro Problems > Math > Algebra > Functions > Geometric Sequences## Arithmetic and Geometric

Two sequences have the same starting value. One sequence is arithmetic and the other is geometric. The common ratio of the geometric sequence is equal to the common difference of the arithmetic sequence. The first term is four times the common ratio/difference. The sum of the first two terms of the geometric sequence is equal to the average of the following quantities:

_{n}

_{n}

Find all possible common differences, if all terms of each sequence are integers.

## Solution

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_{1}- a

_{3}

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