If the first term of a GP is 4 and the common ratio is 1/3, what is the sum of t

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Question: If the first term of a GP is 4 and the common ratio is 1/3, what is the sum of the first three terms?

Options:

Correct Answer: 4.5

Solution:

The first three terms are 4, 4/3, and 4/9. Their sum is 4 + 4/3 + 4/9 = 4 + 1.33 + 0.44 = 5.77.

If the first term of a GP is 4 and the common ratio is 1/3, what is the sum of the first three terms?

If the first term of a GP is 4 and the common ratio is 1/3, what is the sum of the first three terms?

Step 1: Identify the first term of the GP, which is given as 4.
Step 2: Identify the common ratio of the GP, which is given as 1/3.
Step 3: Calculate the second term by multiplying the first term by the common ratio: 4 * (1/3) = 4/3.
Step 4: Calculate the third term by multiplying the second term by the common ratio: (4/3) * (1/3) = 4/9.
Step 5: List the first three terms: 4, 4/3, and 4/9.
Step 6: Find a common denominator to add the fractions: The common denominator for 3 and 9 is 9.
Step 7: Convert 4 to a fraction with a denominator of 9: 4 = 36/9.
Step 8: Convert 4/3 to a fraction with a denominator of 9: 4/3 = 12/9.
Step 9: Now add the fractions: 36/9 + 12/9 + 4/9 = (36 + 12 + 4) / 9 = 52/9.
Step 10: The sum of the first three terms is 52/9, which is approximately 5.77.

Geometric Progression (GP) – Understanding the definition and properties of a geometric progression, including how to find terms and sums.
Sum of a Series – Calculating the sum of a finite series, specifically the first few terms of a geometric series.