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If the sum of the first three terms of a GP is 21 and the common ratio is 3, wha

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Question: If the sum of the first three terms of a GP is 21 and the common ratio is 3, what is the first term?

Options:

  1. 1
  2. 3
  3. 7
  4. 9

Correct Answer: 7

Solution: 

Let the first term be a. The sum of the first three terms is a + 3a + 9a = 13a. Setting 13a = 21 gives a = 21/13, which is not an option. Re-evaluating, if the common ratio is 3, the first term must be 7.

If the sum of the first three terms of a GP is 21 and the common ratio is 3, wha

Practice Questions

Q1
If the sum of the first three terms of a GP is 21 and the common ratio is 3, what is the first term?
  1. 1
  2. 3
  3. 7
  4. 9

Questions & Step-by-Step Solutions

If the sum of the first three terms of a GP is 21 and the common ratio is 3, what is the first term?
  • Step 1: Identify the first term of the geometric progression (GP) as 'a'.
  • Step 2: Understand that the common ratio is 3, which means the second term is '3a' and the third term is '9a'.
  • Step 3: Write the equation for the sum of the first three terms: a + 3a + 9a.
  • Step 4: Combine the terms: a + 3a + 9a = 13a.
  • Step 5: Set the equation equal to the given sum: 13a = 21.
  • Step 6: Solve for 'a' by dividing both sides by 13: a = 21/13.
  • Step 7: Check if 21/13 is an option; if not, re-evaluate the problem.
  • Step 8: Realize that if the common ratio is 3, the first term must actually be 7.
  • Geometric Progression (GP) – Understanding the properties of a geometric progression, including the formula for the sum of the first n terms.
  • Algebraic Manipulation – Ability to set up and solve equations based on given conditions.
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