The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
Correct Answer: Option B
Explanation:
\((1 + kx)^{8} = ^{8}C_{0}(1^{8})(kx)^{0} + ^{8}C_{1}(1^{7})(kx)^{1} + ...\)
The 5th term = \(^{8}C_{5 - 1}(1^{4})(kx)^{4}\)
= \(^{8}C_{4} (kx)^{4}\)
\(\implies 70k^{4} = \frac{35}{8}\)
\(k^{4} = \frac{\frac{35}{8}}{70}\)
\(k^{4} = \frac{1}{16}\)
\(k = \frac{1}{2}\)
\((1 + kx)^{8} = ^{8}C_{0}(1^{8})(kx)^{0} + ^{8}C_{1}(1^{7})(kx)^{1} + ...\)
The 5th term = \(^{8}C_{5 - 1}(1^{4})(kx)^{4}\)
= \(^{8}C_{4} (kx)^{4}\)
\(\implies 70k^{4} = \frac{35}{8}\)
\(k^{4} = \frac{\frac{35}{8}}{70}\)
\(k^{4} = \frac{1}{16}\)
\(k = \frac{1}{2}\)