In a geometric progression, if the 3rd term is 27 and the common ratio is 3, what is the first term?

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Q: In a geometric progression, if the 3rd term is 27 and the common ratio is 3, what is the first term?

Solution: Let the first term be a. The 3rd term is a * r^2 = a * 3^2 = 9a. Setting 9a = 27 gives a = 3.

Steps: 8

Step 1: Identify the first term of the geometric progression as 'a'.
Step 2: Understand that the common ratio is given as 3.
Step 3: Recall the formula for the nth term of a geometric progression, which is: nth term = first term * (common ratio)^(n-1).
Step 4: For the 3rd term, use the formula: 3rd term = a * (3)^(3-1) = a * 3^2.
Step 5: Calculate 3^2, which equals 9. So, the 3rd term can be written as: 3rd term = a * 9.
Step 6: We know from the question that the 3rd term is 27, so set up the equation: 9a = 27.
Step 7: Solve for 'a' by dividing both sides of the equation by 9: a = 27 / 9.
Step 8: Calculate 27 divided by 9, which equals 3. Therefore, the first term 'a' is 3.