If the first term of a geometric progression is 3 and the common ratio is 2, wha

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Question: If the first term of a geometric progression is 3 and the common ratio is 2, what is the 4th term?

Options:

Correct Answer: 24

Solution:

The nth term of a geometric progression is given by a_n = a * r^(n-1). Here, a = 3, r = 2, and n = 4. So, a_4 = 3 * 2^(4-1) = 3 * 2^3 = 3 * 8 = 24.

If the first term of a geometric progression is 3 and the common ratio is 2, what is the 4th term?

If the first term of a geometric progression is 3 and the common ratio is 2, what is the 4th term?

Step 1: Identify the first term (a) of the geometric progression, which is given as 3.
Step 2: Identify the common ratio (r) of the geometric progression, which is given as 2.
Step 3: Identify the term number (n) we want to find, which is the 4th term, so n = 4.
Step 4: Use the formula for the nth term of a geometric progression: a_n = a * r^(n-1).
Step 5: Substitute the values into the formula: a_4 = 3 * 2^(4-1).
Step 6: Calculate the exponent: 4 - 1 = 3, so we have a_4 = 3 * 2^3.
Step 7: Calculate 2^3, which is 8.
Step 8: Multiply 3 by 8: 3 * 8 = 24.
Step 9: The 4th term of the geometric progression is 24.

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