An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, ... . Find the n\(^{th}\)...
FURTHER MATHEMATICS
WAEC 2023
An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, ... . Find the n\(^{th}\) term of the sequence
- A. \(8\sqrt2^n\)
- B. \(2^{(n+2)}\sqrt2\)
- C. \(\sqrt2^{(n+3)}\)
- D. \(8n\sqrt2\)
Correct Answer: B. \(2^{(n+2)}\sqrt2\)
Explanation
8√2, 16√2, 32√2, ..
\(a = 8\sqrt2; r =\frac{T_2}{T_1}=\frac{16\sqrt2}{8\sqrt2}=2\)
\(T_n=ar^{n-1}\)
\(T_n=8\sqrt2 \times 2^{n-1}\)
\(T_n=2^3\times2^{n-1}\times\sqrt2\)
\(T_n=2^{3+n-1}\times\sqrt2\)
\(\therefore T_n= 2^{(n+2)}\sqrt2\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *