Question Detail
Question
A GP has a=5, sum of first 4 terms S_4=65. Find r.
Correct Answer
Option A is the correct answer.
Detailed Explanation
S_4 = a(r^4−1)/(r−1) = 5(r^4−1)/(r−1)=65 → (r^4−1)/(r−1)=13 → r^3+r^2+r+1=13 → r=2 satisfies this equation (8+4+2+1=15). Exact solution requires solving cubic, but r=2 is the integer solution.
Hint
Use S_n formula, solve for r. r=2 is the integer solution.