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

₹0.0

Question: In a geometric progression, if the first term is x and the common ratio is y, what is the expression for the 3rd term?

Options:

Correct Answer: xy^2

Solution:

The 3rd term of a GP is given by a * r^(n-1). Here, it is x * y^(3-1) = xy^2.

In a geometric progression, if the first term is x and the common ratio is y, what is the expression for the 3rd term?

In a geometric progression, if the first term is x and the common ratio is y, what is the expression for the 3rd term?

Step 1: Understand that a geometric progression (GP) is a sequence where each term is found by multiplying the previous term by a constant called the common ratio.
Step 2: Identify the first term of the GP, which is given as 'x'.
Step 3: Identify the common ratio of the GP, which is given as 'y'.
Step 4: Recall the formula for the nth term of a GP, which is: a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.
Step 5: For the 3rd term, set n = 3 in the formula. So, it becomes: x * y^(3-1).
Step 6: Simplify the exponent: 3 - 1 = 2. Therefore, the expression becomes: x * y^2.
Step 7: Write the final expression for the 3rd term as: xy^2.

Geometric Progression – 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.
Formula for nth term – The nth term of a geometric progression can be calculated using the formula a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.