If the second term of a GP is 8 and the fourth term is 32, what is the common ra

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Question: If the second term of a GP is 8 and the fourth term is 32, what is the common ratio?

Options:

Correct Answer: 2

Solution:

Let the first term be a and the common ratio be r. Then, 8 = ar and 32 = ar^3. Dividing these gives r^2 = 4, so r = 2.

If the second term of a GP is 8 and the fourth term is 32, what is the common ratio?

If the second term of a GP is 8 and the fourth term is 32, what is the common ratio?

Step 1: Identify the terms of the geometric progression (GP). The second term is given as 8 and the fourth term is given as 32.
Step 2: Let the first term of the GP be 'a' and the common ratio be 'r'.
Step 3: Write the equation for the second term: 8 = a * r.
Step 4: Write the equation for the fourth term: 32 = a * r^3.
Step 5: Now, we have two equations: 8 = a * r and 32 = a * r^3.
Step 6: To find the common ratio 'r', divide the second equation by the first equation: (a * r^3) / (a * r) = 32 / 8.
Step 7: Simplify the left side: r^2 = 32 / 8.
Step 8: Calculate the right side: 32 / 8 = 4, so r^2 = 4.
Step 9: Take the square root of both sides to find 'r': r = 2.

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.
Term Relationships in GP – Understanding how to express terms of a GP in relation to the first term and the common ratio.
Algebraic Manipulation – The ability to manipulate equations to isolate variables and solve for unknowns.