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If the first term of a geometric series is 4 and the common ratio is 2, what is
If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?
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Q1
If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?
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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.
Questions & Step-by-step Solutions
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Q
Q: If the first term of a geometric series is 4 and the common ratio is 2, what is the 7th term?
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.
Steps: 8
Show Steps
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.
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