In a geometric progression, if the 1st term is 4 and the 5th term is 64, what is

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Question: In a geometric progression, if the 1st term is 4 and the 5th term is 64, what is the common ratio?

Options:

Correct Answer: 4

Solution:

Let the common ratio be r. The 5th term is given by ar^4 = 64. Thus, 4r^4 = 64 => r^4 = 16 => r = 2.

In a geometric progression, if the 1st term is 4 and the 5th term is 64, what is the common ratio?

In a geometric progression, if the 1st term is 4 and the 5th term is 64, what is the common ratio?

Step 1: Identify the first term of the geometric progression, which is given as 4.
Step 2: Identify the 5th term of the geometric progression, which is given as 64.
Step 3: Use the formula for the nth term of a geometric progression, which is a * r^(n-1). Here, a is the first term, r is the common ratio, and n is the term number.
Step 4: For the 5th term, we have a * r^(5-1) = 64. Substitute a = 4: 4 * r^4 = 64.
Step 5: To isolate r^4, divide both sides of the equation by 4: r^4 = 64 / 4.
Step 6: Simplify the right side: r^4 = 16.
Step 7: To find r, take the fourth root of both sides: r = 2.

Geometric Progression – A sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio.
Finding Terms – Understanding how to express terms in a geometric progression using the first term and the common ratio.
Exponents – Knowledge of manipulating and solving equations involving exponents.