JAMB - Mathematics (2025 - No. 29)
The second and fifth terms of a G.P are 1 and \(\frac{1}{8}\) respectively. Find the common ratio
\(\frac{1}{4}\)
\(\frac{1}{5}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
설명
Let the first term be \( a \), and the common ratio be \( r \). Given:
- Second term: \( ar = 1 \)
- Fifth term: \( ar^4 = \frac{1}{8} \)
From the first equation, we have: \(a = \frac{1}{r}\)
Substituting into the second equation:
\(\frac{1}{r} r^4 = \frac{1}{8}\)
\(r^3 = \frac{1}{8}\)
Taking the cube root gives:
\(r = \frac{1}{2}\)
Thus, the common ratio is \(\frac{1}{2}\)