Sequence and Series
Geometric Progression
JEE Main 2019
Grade 11
Question:
Let $a_1, a_2, \dots , a_{10}$ be in G.P. If $\frac{a_3}{a_1} = 25$, then $\frac{a_9}{a_5}$ equals:
(1) $5^4$
(2) $4^5$
(3) $5^3$
(4) $2^5$
Step-by-Step Solution
Key Concept: $a_3/a_1 = r^2 = 25$ gives the common ratio $r$. Then $a_9/a_5 = r^{9-5} = r^4$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)