In a GP, if the first term is 5 and the common ratio is 1/2, what is the sum of

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Question: In a GP, if the first term is 5 and the common ratio is 1/2, what is the sum of the first four terms?

Options:

Correct Answer: 12.5

Solution:

The first four terms are 5, 2.5, 1.25, and 0.625. Their sum is 5 + 2.5 + 1.25 + 0.625 = 9.375.

In a GP, if the first term is 5 and the common ratio is 1/2, what is the sum of the first four terms?

In a GP, if the first term is 5 and the common ratio is 1/2, what is the sum of the first four terms?

Step 1: Identify the first term of the GP, which is given as 5.
Step 2: Identify the common ratio of the GP, which is given as 1/2.
Step 3: Calculate the second term by multiplying the first term by the common ratio: 5 * (1/2) = 2.5.
Step 4: Calculate the third term by multiplying the second term by the common ratio: 2.5 * (1/2) = 1.25.
Step 5: Calculate the fourth term by multiplying the third term by the common ratio: 1.25 * (1/2) = 0.625.
Step 6: List the first four terms: 5, 2.5, 1.25, and 0.625.
Step 7: Add the first four terms together: 5 + 2.5 + 1.25 + 0.625.
Step 8: Calculate the sum: 5 + 2.5 = 7.5, then 7.5 + 1.25 = 8.75, and finally 8.75 + 0.625 = 9.375.

Geometric Progression (GP) – A sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Sum of Terms in a GP – The sum of the first n terms of a geometric progression can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.