In a geometric progression, if the first term is 5 and the last term is 80, and

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Question: In a geometric progression, if the first term is 5 and the last term is 80, and there are 4 terms in total, what is the common ratio?

Options:

Correct Answer: 2

Solution:

Let the common ratio be r. The terms are 5, 5r, 5r^2, 5r^3. Setting 5r^3 = 80 gives r^3 = 16, thus r = 2.

In a geometric progression, if the first term is 5 and the last term is 80, and there are 4 terms in total, what is the common ratio?

In a geometric progression, if the first term is 5 and the last term is 80, and there are 4 terms in total, what is the common ratio?

Step 1: Identify the first term of the geometric progression, which is given as 5.
Step 2: Identify the last term of the geometric progression, which is given as 80.
Step 3: Note that there are 4 terms in total in the geometric progression.
Step 4: Write the terms of the geometric progression using the first term and the common ratio (r): The terms are 5, 5r, 5r^2, and 5r^3.
Step 5: Since the last term (5r^3) is equal to 80, set up the equation: 5r^3 = 80.
Step 6: To solve for r^3, divide both sides of the equation by 5: r^3 = 80 / 5.
Step 7: Simplify the right side: r^3 = 16.
Step 8: To find r, take the cube root of both sides: r = cube root of 16.
Step 9: Calculate the cube root of 16, which is 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.
Finding the Common Ratio – The process of determining the ratio between consecutive terms in a geometric sequence.
Exponential Equations – Equations where the variable appears in the exponent, requiring manipulation to isolate the variable.