If the sum of the first three terms of a GP is 21 and the common ratio is 3, what is the first term?
Practice Questions
1 question
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?
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7
9
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.
Questions & Step-by-step Solutions
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Q
Q: If the sum of the first three terms of a GP is 21 and the common ratio is 3, what is the first term?
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.
Steps: 8
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.
