Google
Câu hỏi: Cho cấp số cộng $\left( {{u}_{n}} \right)$ có ${{u}_{3}}=5;\!\!~\!\!{{u}_{5}}=9$. Tính ${{u}_{15}}$.
A. ${{u}_{15}}=-29$.
B. ${{u}_{15}}=4$.
C. ${{u}_{15}}=45$.
D. ${{u}_{15}}=29$.
A. ${{u}_{15}}=-29$.
B. ${{u}_{15}}=4$.
C. ${{u}_{15}}=45$.
D. ${{u}_{15}}=29$.
Ta có $\left\{ \begin{aligned}
& {{u}_{3}}=5 \\
& {{u}_{5}}=9 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& {{u}_{1}}+2d=5 \\
& {{u}_{1}}+4d=9 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& {{u}_{1}}=1 \\
& d=2 \\
\end{aligned} \right.$.
Khi đó ${{u}_{15}}={{u}_{1}}+14d=1+14.2=29$.
& {{u}_{3}}=5 \\
& {{u}_{5}}=9 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& {{u}_{1}}+2d=5 \\
& {{u}_{1}}+4d=9 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& {{u}_{1}}=1 \\
& d=2 \\
\end{aligned} \right.$.
Khi đó ${{u}_{15}}={{u}_{1}}+14d=1+14.2=29$.
Đáp án D.
