In a geometric progression, if the first term is x and the common ratio is r, wh

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Question: In a geometric progression, if the first term is x and the common ratio is r, what is the expression for the sum of the first n terms?

Options:

Correct Answer: x(1 - r^n)/(1 - r)

Solution:

The sum of the first n terms of a GP is given by S_n = a(1 - r^n)/(1 - r) for r ≠ 1.

In a geometric progression, if the first term is x and the common ratio is r, what is the expression for the sum of the first n terms?

In a geometric progression, if the first term is x and the common ratio is r, what is the expression for the sum of the first n terms?

Step 1: Identify the first term of the geometric progression (GP), which is given as x.
Step 2: Identify the common ratio of the GP, which is given as r.
Step 3: Understand that the sum of the first n terms of a GP can be calculated using a specific formula.
Step 4: The formula for the sum of the first n terms (S_n) is S_n = a(1 - r^n) / (1 - r), where a is the first term.
Step 5: Substitute the first term (x) into the formula, so it becomes S_n = x(1 - r^n) / (1 - r).
Step 6: Note that this formula is valid only when the common ratio (r) is not equal to 1.

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 a Geometric Series – The formula for the sum of the first n terms of a geometric progression, which varies depending on whether the common ratio is equal to 1 or not.