If the sum of the first three terms of a geometric progression is 14 and the com

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Question: If the sum of the first three terms of a geometric progression is 14 and the common ratio is 2, what is the first term?

Options:

Correct Answer: 3

Solution:

Let the first term be a. The sum of the first three terms is a + 2a + 4a = 7a. Setting 7a = 14 gives a = 2.

If the sum of the first three terms of a geometric progression is 14 and the common ratio is 2, what is the first term?

If the sum of the first three terms of a geometric progression is 14 and the common ratio is 2, what is the first term?

Step 1: Identify the first term of the geometric progression as 'a'.
Step 2: Recognize that the common ratio is 2, which means the second term is '2a' and the third term is '4a'.
Step 3: Write the equation for the sum of the first three terms: a + 2a + 4a.
Step 4: Combine the terms: a + 2a + 4a = 7a.
Step 5: Set the equation equal to 14, since the sum of the first three terms is given as 14: 7a = 14.
Step 6: Solve for 'a' by dividing both sides of the equation by 7: a = 14 / 7.
Step 7: Calculate the value: a = 2.

Geometric Progression – Understanding the properties of geometric sequences, including the relationship between the first term and the common ratio.
Sum of Terms – Calculating the sum of the first few terms in a geometric progression using the formula for the sum.
Algebraic Manipulation – Solving equations to find unknown variables, in this case, the first term of the geometric progression.