If the first term of a GP is x and the common ratio is y, which of the following

₹0.0

Question: If the first term of a GP is x and the common ratio is y, which of the following represents the 4th term?

Options:

Correct Answer: xy^3

Solution:

The nth term of a GP is given by a * r^(n-1). Thus, the 4th term is x * y^(4-1) = xy^3.

If the first term of a GP is x and the common ratio is y, which of the following represents the 4th term?

If the first term of a GP is x and the common ratio is y, which of the following represents the 4th term?

Step 1: Understand that a GP (Geometric Progression) has a first term and a common ratio.
Step 2: Identify the first term, which is given as 'x'.
Step 3: Identify the common ratio, which is given as 'y'.
Step 4: Recall the formula for the nth term of a GP, which is: nth term = first term * (common ratio)^(n-1).
Step 5: To find the 4th term, set n = 4 in the formula.
Step 6: Substitute the values into the formula: 4th term = x * y^(4-1).
Step 7: Simplify the exponent: 4-1 = 3, so the formula becomes 4th term = x * y^3.
Step 8: Write the final answer as xy^3.

Geometric Progression (GP) – A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Nth Term Formula – The formula for the nth term of a GP is given by a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.