Sequences & Series
Geometric Progression — Product Expression
nta_pyq_2023_apr
Grade 11
Question:
Let $a_1,a_2,a_3,\ldots$ be an increasing GP. If $a_6+a_8=2$ and $a_3\cdot a_5=\frac{1}{9}$, then $6(a_2+a_4)(a_4+a_6)$ is equal to
Step-by-Step Solution
Key Concept: Let $a_k=ar^{k-1}$. $a_3\cdot a_5=a^2r^6=\frac{1}{9}\Rightarrow ar^3=\frac{1}{3}$. From $a_6+a_8=2$: $ar^5+ar^7=2\Rightarrow ar^3\cdot r^2(1+r^2)=2$.
$3$.
Correct Answer: 1