What is the sum of the first 5 terms of a GP where the first term is 2 and the c

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Question: What is the sum of the first 5 terms of a GP where the first term is 2 and the common ratio is 3?

Options:

Correct Answer: 242

Solution:

The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_5 = 2(1 - 3^5) / (1 - 3) = 2(1 - 243) / (-2) = 242.

What is the sum of the first 5 terms of a GP where the first term is 2 and the common ratio is 3?

What is the sum of the first 5 terms of a GP where the first term is 2 and the common ratio is 3?

Step 1: Identify the first term (a) of the GP, which is given as 2.
Step 2: Identify the common ratio (r) of the GP, which is given as 3.
Step 3: Identify the number of terms (n) we want to sum, which is 5.
Step 4: Use the formula for the sum of the first n terms of a GP: S_n = a(1 - r^n) / (1 - r).
Step 5: Substitute the values into the formula: S_5 = 2(1 - 3^5) / (1 - 3).
Step 6: Calculate 3^5, which is 243.
Step 7: Substitute 243 back into the equation: S_5 = 2(1 - 243) / (1 - 3).
Step 8: Simplify the equation: S_5 = 2(-242) / (-2).
Step 9: Calculate the final result: S_5 = 242.

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