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

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

Options:

Correct Answer: 2

Solution:

The last term can be expressed as a * r^(n-1). Here, 80 = 5 * r^(4-1) = 5 * r^3. Thus, r^3 = 16, giving r = 2.

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

Step 1: Identify the first term (a) 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: Determine the number of terms (n) in the geometric progression, which is given as 4.
Step 4: Use the formula for the last term of a geometric progression: last term = a * r^(n-1).
Step 5: Substitute the known values into the formula: 80 = 5 * r^(4-1).
Step 6: Simplify the equation: 80 = 5 * r^3.
Step 7: Divide both sides by 5 to isolate r^3: 80 / 5 = r^3, which simplifies to 16 = r^3.
Step 8: Find the value of r by taking the cube root of both sides: r = 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.
Formula for the nth term – The nth term of a geometric progression can be calculated using the formula a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.