In a geometric series where the first term is 4 and the common ratio is 2, what

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Question: In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (2023)

Options:

Correct Answer: 256

Exam Year: 2023

Solution:

The nth term of a geometric series is given by ar^(n-1). Here, a = 4, r = 2, n = 6. So, 4 * 2^(6-1) = 4 * 32 = 128.

In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (2023)

In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (2023)

Step 1: Identify the first term (a) of the geometric series. In this case, a = 4.
Step 2: Identify the common ratio (r) of the geometric series. Here, r = 2.
Step 3: Identify which term (n) you want to find. We want the 6th term, so n = 6.
Step 4: Use the formula for the nth term of a geometric series, which is a * r^(n-1).
Step 5: Substitute the values into the formula: 4 * 2^(6-1).
Step 6: Calculate the exponent: 6 - 1 = 5, so we have 4 * 2^5.
Step 7: Calculate 2^5, which is 32.
Step 8: Multiply 4 by 32 to get the 6th term: 4 * 32 = 128.

Geometric Series – 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 series is given by ar^(n-1), where a is the first term, r is the common ratio, and n is the term number.