The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

Explanation

To solve the problem step by step, let's denote the first term of the geometric progression as \( a \) and the common ratio as \( r \).

### Step 1: Set up the equations based on the problem statement
According to the problem, we have two conditions:
1. The sum of the first two terms is 12:
\[ a + ar = 12 \quad \text{(Equation 1)} \]
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