Question: In a GP, if the first term is x and the common ratio is y, what is the expression for the 6th term?
Options:
xy^5
xy^6
x^6y
x^5y
Correct Answer: xy^5
Solution:
The nth term of a GP is given by a * r^(n-1). Thus, the 6th term = x * y^(6-1) = xy^5.
In a GP, if the first term is x and the common ratio is y, what is the expressio
Practice Questions
Q1
In a GP, if the first term is x and the common ratio is y, what is the expression for the 6th term?
xy^5
xy^6
x^6y
x^5y
Questions & Step-by-Step Solutions
In a GP, if the first term is x and the common ratio is y, what is the expression for the 6th term?
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: Substitute 'x' for the first term and 'y' for the common ratio in the formula.
Step 6: For the 6th term, set n = 6 in the formula: 6th term = x * y^(6-1).
Step 7: Simplify the exponent: 6 - 1 = 5, so the expression becomes 6th term = x * y^5.
Step 8: Write the final expression for the 6th term as xy^5.
Geometric Progression (GP) – A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Nth Term Formula – The formula for the nth term of a GP is given by a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.
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