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If the first term of a GP is x and the common ratio is y, which of the following
If the first term of a GP is x and the common ratio is y, which of the following represents the 4th term?
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Practice Questions
1 question
Q1
If the first term of a GP is x and the common ratio is y, which of the following represents the 4th term?
xy^3
x^3y
x^4y
xy^4
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The nth term of a GP is given by a * r^(n-1). Thus, the 4th term is x * y^(4-1) = xy^3.
Questions & Step-by-step Solutions
1 item
Q
Q: If the first term of a GP is x and the common ratio is y, which of the following represents the 4th term?
Solution:
The nth term of a GP is given by a * r^(n-1). Thus, the 4th term is x * y^(4-1) = xy^3.
Steps: 8
Show Steps
Step 1: Understand that a GP (Geometric Progression) has a first term and a common ratio.
Step 2: Identify the first term, which is given as 'x'.
Step 3: Identify the common ratio, which is given as 'y'.
Step 4: Recall the formula for the nth term of a GP, which is: nth term = first term * (common ratio)^(n-1).
Step 5: To find the 4th term, set n = 4 in the formula.
Step 6: Substitute the values into the formula: 4th term = x * y^(4-1).
Step 7: Simplify the exponent: 4-1 = 3, so the formula becomes 4th term = x * y^3.
Step 8: Write the final answer as xy^3.
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