In a geometric progression, if the first term is x and the common ratio is y, wh
Practice Questions
Q1
In a geometric progression, if the first term is x and the common ratio is y, what is the expression for the 3rd term?
xy^2
x/y^2
x^2y
x^2/y
Questions & Step-by-Step Solutions
In a geometric progression, if the first term is x and the common ratio is y, what is the expression for the 3rd term?
Step 1: Understand that a geometric progression (GP) is a sequence where each term is found by multiplying the previous term by a constant called the common ratio.
Step 2: Identify the first term of the GP, which is given as 'x'.
Step 3: Identify the common ratio of the GP, which is given as 'y'.
Step 4: 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 5: For the 3rd term, set n = 3 in the formula. So, it becomes: x * y^(3-1).
Step 6: Simplify the exponent: 3 - 1 = 2. Therefore, the expression becomes: x * y^2.
Step 7: Write the final expression for the 3rd term as: xy^2.
