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If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?
If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?
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Practice Questions
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Q1
If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?
3
9
1
27
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Let the first term be a. Then, the 3rd term is ar^2 = 27. Thus, a * 3^2 = 27, giving a = 3.
Questions & Step-by-step Solutions
1 item
Q
Q: If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?
Solution:
Let the first term be a. Then, the 3rd term is ar^2 = 27. Thus, a * 3^2 = 27, giving a = 3.
Steps: 9
Show Steps
Step 1: Identify the first term of the geometric progression (GP) as 'a'.
Step 2: Understand that the common ratio (r) is given as 3.
Step 3: Recall the formula for the nth term of a GP, which is a * r^(n-1).
Step 4: Since we need the 3rd term, set n = 3. The formula becomes: 3rd term = a * r^(3-1) = a * r^2.
Step 5: Substitute the common ratio into the formula: 3rd term = a * 3^2.
Step 6: We know the 3rd term is 27, so set up the equation: a * 3^2 = 27.
Step 7: Calculate 3^2, which is 9. Now the equation is: a * 9 = 27.
Step 8: To find 'a', divide both sides of the equation by 9: a = 27 / 9.
Step 9: Simplify the division: a = 3.
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