If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?

If the 3rd term of a GP is 27 and the common ratio is 3, what is the first term?

Step 1: Identify the first term of the geometric progression (GP) as 'a'.
Step 2: Understand that the common ratio (r) is given as 3.
Step 3: Recall the formula for the nth term of a GP, which is a * r^(n-1).
Step 4: Since we need the 3rd term, set n = 3. The formula becomes: 3rd term = a * r^(3-1) = a * r^2.
Step 5: Substitute the common ratio into the formula: 3rd term = a * 3^2.
Step 6: We know the 3rd term is 27, so set up the equation: a * 3^2 = 27.
Step 7: Calculate 3^2, which is 9. Now the equation is: a * 9 = 27.
Step 8: To find 'a', divide both sides of the equation by 9: a = 27 / 9.
Step 9: Simplify the division: a = 3.

Geometric Progression (GP) – Understanding the formula for the nth term of a geometric progression, which is given by a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.
Solving for Variables – The ability to isolate and solve for the first term in a geometric progression using given terms and the common ratio.