In a geometric progression, if the first term is 3 and the common ratio is 2, wh

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Question: In a geometric progression, if the first term is 3 and the common ratio is 2, what is the 5th term?

Options:

Correct Answer: 48

Solution:

The nth term of a GP is given by a * r^(n-1). Here, a = 3, r = 2, and n = 5. Thus, the 5th term = 3 * 2^(5-1) = 3 * 16 = 48.

In a geometric progression, if the first term is 3 and the common ratio is 2, what is the 5th term?

In a geometric progression, if the first term is 3 and the common ratio is 2, what is the 5th term?

Step 1: Identify the first term (a) of the geometric progression. Here, a = 3.
Step 2: Identify the common ratio (r) of the geometric progression. Here, r = 2.
Step 3: Identify the term number (n) for which we want to find the value. Here, n = 5.
Step 4: Use the formula for the nth term of a geometric progression, which is a * r^(n-1).
Step 5: Substitute the values into the formula: 3 * 2^(5-1).
Step 6: Calculate the exponent: 5 - 1 = 4, so we have 3 * 2^4.
Step 7: Calculate 2^4, which is 16.
Step 8: Multiply 3 by 16 to get the 5th term: 3 * 16 = 48.

Geometric Progression (GP) – 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.
Nth Term Formula – The formula for finding the nth term of a geometric progression, given by a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.