If the first term of a geometric progression is x and the common ratio is 3, whi

₹0.0

Question: If the first term of a geometric progression is x and the common ratio is 3, which of the following represents the 6th term?

Options:

Correct Answer: x * 3^5

Solution:

The nth term of a GP is given by a * r^(n-1). Here, the 6th term = x * 3^(6-1) = x * 3^5.

If the first term of a geometric progression is x and the common ratio is 3, which of the following represents the 6th term?

If the first term of a geometric progression is x and the common ratio is 3, which of the following represents the 6th term?

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 3.
Step 3: 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 4: Substitute the values into the formula for the 6th term. Here, a = x, r = 3, and n = 6.
Step 5: The formula becomes: 6th term = x * 3^(6-1).
Step 6: Simplify the exponent: 6 - 1 = 5, so it becomes 6th term = x * 3^5.

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 geometric progression is given by a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.