csat-suneung 2025 Q2

csat-suneung · South-Korea · csat__math 3 marks Geometric Sequences and Series Finite Geometric Sum and Term Relationships
A geometric sequence $\left\{ a_{n} \right\}$ with first term and common ratio both equal to a positive number $k$ satisfies $$\frac{a_{4}}{a_{2}} + \frac{a_{2}}{a_{1}} = 30$$ What is the value of $k$? [3 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
A geometric sequence $\left\{ a_{n} \right\}$ with first term and common ratio both equal to a positive number $k$ satisfies
$$\frac{a_{4}}{a_{2}} + \frac{a_{2}}{a_{1}} = 30$$
What is the value of $k$? [3 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5