If the first term of a geometric series is 4 and the common ratio is 2, what is

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Question: If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?

Options:

Correct Answer: 256

Solution:

The nth term of a geometric series is given by a_n = ar^(n-1). Here, a = 4, r = 2, n = 7. So, a_7 = 4 * 2^(7-1) = 4 * 64 = 256.

If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?

If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?

Step 1: Identify the first term of the geometric series, which is given as 4. This is 'a'.
Step 2: Identify the common ratio of the geometric series, which is given as 2. This is 'r'.
Step 3: Identify the term number we want to find, which is the 7th term. This is 'n'.
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_7 = 4 * 2^(7-1).
Step 6: Calculate the exponent: 7 - 1 = 6, so we have a_7 = 4 * 2^6.
Step 7: Calculate 2^6, which is 64.
Step 8: Multiply 4 by 64 to find the 7th term: 4 * 64 = 256.

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 a_n = ar^(n-1), where a is the first term, r is the common ratio, and n is the term number.