AIEEE 2002 (Offline)Question 1
Fifth term of a GP is $2$, then the product of its first $9$ terms is
Sequence and Series · Geometric Progression
Solution
Formulas used. (1) In a G.P., $a_ka_{10-k}=a_5^2$Step 1 - Pair the terms. $a_1a_9=a_2a_8=a_3a_7=a_4a_6=a_5^2$. Step 2 - Product. $$a_1a_2\cdots a_9=\left(a_5^2\right)^4\cdot a_5=a_5^9=2^9=512 .$$ Answer: (B)