In a geometric series, if the first term is 4 and the common ratio is 3, what is

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Question: In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th term?

Options:

Correct Answer: 108

Solution:

The nth term of a geometric series is given by a_n = ar^(n-1). Thus, a_4 = 4 * 3^(4-1) = 4 * 27 = 108.

In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th term?

In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th term?

Step 1: Identify the first term of the geometric series, which is given as 4.
Step 2: Identify the common ratio of the geometric series, which is given as 3.
Step 3: Determine which term we want to find. In this case, we want the 4th term.
Step 4: Use the formula for the nth term of a geometric series, which is a_n = ar^(n-1).
Step 5: Substitute the values into the formula: a_4 = 4 * 3^(4-1).
Step 6: Calculate the exponent: 4 - 1 = 3, so we have a_4 = 4 * 3^3.
Step 7: Calculate 3^3, which is 27.
Step 8: Multiply 4 by 27 to find the 4th term: 4 * 27 = 108.

Geometric Series – A sequence 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 the nth term of a geometric series is given by a_n = ar^(n-1), where 'a' is the first term and 'r' is the common ratio.