In a GP, if the first term is 5 and the last term is 80, and there are 4 terms i

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Question: In a GP, 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 GP, 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 GP, 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 GP, which is given as 5.
Step 2: Identify the last term of the GP, which is given as 80.
Step 3: Note that there are 4 terms in total in the GP.
Step 4: Write the terms of the GP 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 (GP) – Understanding the properties of a geometric progression, including the first term, common ratio, and the relationship between terms.
Exponential Equations – Solving equations involving exponents, particularly in the context of finding the common ratio from the last term.