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If the first term of a geometric progression is x and the common ratio is 3, whi
If the first term of a geometric progression is x and the common ratio is 3, which of the following represents the 6th term?
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Practice Questions
1 question
Q1
If the first term of a geometric progression is x and the common ratio is 3, which of the following represents the 6th term?
x * 3^5
x * 3^6
3 * x^5
3 * x^6
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The nth term of a GP is given by a * r^(n-1). Here, the 6th term = x * 3^(6-1) = x * 3^5.
Questions & Step-by-step Solutions
1 item
Q
Q: If the first term of a geometric progression is x and the common ratio is 3, which of the following represents the 6th term?
Solution:
The nth term of a GP is given by a * r^(n-1). Here, the 6th term = x * 3^(6-1) = x * 3^5.
Steps: 6
Show Steps
Step 1: Identify the first term of the geometric progression (GP), which is given as x.
Step 2: Identify the common ratio of the GP, which is given as 3.
Step 3: Recall the formula for the nth term of a GP, which is a * r^(n-1), where a is the first term, r is the common ratio, and n is the term number.
Step 4: Substitute the values into the formula for the 6th term. Here, a = x, r = 3, and n = 6.
Step 5: The formula becomes: 6th term = x * 3^(6-1).
Step 6: Simplify the exponent: 6 - 1 = 5, so it becomes 6th term = x * 3^5.
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