If the 2nd term of a geometric progression is 8 and the 4th term is 32, what is

If the 2nd term of a geometric progression is 8 and the 4th term is 32, what is the common ratio?

If the 2nd term of a geometric progression is 8 and the 4th term is 32, what is the common ratio?

Step 1: Identify the terms of the geometric progression. The 2nd term is given as 8 and the 4th term is given as 32.
Step 2: Let the first term be 'a' and the common ratio be 'r'.
Step 3: Write the equation for the 2nd term: ar = 8.
Step 4: Write the equation for the 4th term: ar^3 = 32.
Step 5: Now you have two equations: ar = 8 and ar^3 = 32.
Step 6: To find the common ratio, divide the equation for the 4th term by the equation for the 2nd term: (ar^3) / (ar) = 32 / 8.
Step 7: Simplify the left side: r^2 = 32 / 8.
Step 8: Calculate the right side: 32 / 8 = 4, so r^2 = 4.
Step 9: Take the square root of both sides to find r: r = 2.

Geometric Progression – A sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio.
Term Identification – Understanding how to identify and express terms in a geometric progression using the first term and common ratio.
Algebraic Manipulation – The ability to manipulate equations to isolate variables and solve for unknowns.