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In a geometric series where the first term is 4 and the common ratio is 2, what
In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (2023)
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Q1
In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (2023)
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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.
Questions & Step-by-step Solutions
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Q
Q: In a geometric series where the first term is 4 and the common ratio is 2, what is the 6th term? (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.
Steps: 8
Show Steps
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.
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