If the sum of the first three terms of a GP is 14 and the common ratio is 2, wha
Practice Questions
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If the sum of the first three terms of a GP is 14 and the common ratio is 2, what is the first term?
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Questions & Step-by-Step Solutions
If the sum of the first three terms of a GP is 14 and the common ratio is 2, what is the first term?
Step 1: Identify the first term of the geometric progression (GP) as 'a'.
Step 2: The common ratio is given as 2. This 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 sum equal to 14: 7a = 14.
Step 6: Solve for 'a' by dividing both sides by 7: a = 14 / 7.
Step 7: Calculate the value: a = 2.
Geometric Progression (GP) – Understanding the properties of a geometric progression, including the relationship between the first term and the common ratio.
Sum of Terms in a GP – Calculating the sum of the first few terms in a geometric progression using the formula for the sum.
