If the first term of a geometric sequence is 3 and the common ratio is 2, what i

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

Options:

Correct Answer: 24

Solution:

The nth term of a geometric sequence is a * r^(n-1). Here, a = 3, r = 2, n = 4. So, 3 * 2^(4-1) = 3 * 8 = 24.

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

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

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

Geometric Sequence – A sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio.
Nth Term Formula – The formula for finding the nth term of a geometric sequence is given by a * r^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the term number.