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2,4,8,14,......... tentukan 2 suku berikutnya​

Berikut ini adalah pertanyaan dari nyomansunarti55 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

2,4,8,14,.........
tentukan 2 suku berikutnya​

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

\mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}

2, 4, 8, 14, 22, 32

------------------

\mathbb{ \color{orange}{ \underbrace{PENYELESAIAN}}}

\small \boxed{ \begin{array}{c|c} \color{violet} \bf Rumus& \color{violet} \bf Keterangan \\ \hline & \tt{\color{red} U} {\color{lightgreen}_n} = suku \: ke - n ~~~~~~~~~~~\\ & \tt {\color{lightgreen}n} = banyak \: suku~~~~~~~~ \\ \boxed{ \: \color{orange} \tt {\color{red} U}{\color{lightgreen}_n} = {\color{magenta}a} + { \color{gold}b} ( {\color{lightgreen}n} - 1) + \small{ \frac{{ \color{aqua}c}({\color{lightgreen}n} - 1)({\color{lightgreen}n} - 2)}{2} } \: } &\tt {\color{magenta}a} = suku \: pertama~~~~~~ \\ & \tt { \color{gold}b} = beda \: (U_{2} - U_{1}) ~~~~~\\ & \tt {\color{aqua}c} = beda \: (tingkat \: 1) \end{array} } \\ \\

\boxed{ \: \begin{aligned} &\tt {\bf2} \: \: \: 4 \: \: \: 8 \: \: \: 14 \: \: \: ... \begin{aligned} &\Rightarrow& \bf a = 2\end{aligned} \\ &\tt \: \: \: {\bf 2} \: \: \: 4 \: \: \: 6 \: \: \: ... \: \: \: \: \begin{aligned} &\Rightarrow& \bf b = 2\end{aligned} \\ & \: \: \: \: \: \: \tt{ \bf2} \: \: \: 2 \: \: \: ... \: \: \: \: \: \: \begin{aligned} &\Rightarrow& \bf \: c = 2\end{aligned} \end{aligned} \: } \\\\

  • rumus suku ke-n :

\begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_n &= \tt a + b(n - 1) + \small{ \frac{c(n - 1)(n - 2)}{2}} \\ \tt U_n &= \tt 2 + 2(n - 1) + \small{ \frac{ \not2(n - 1)(n - 2)}{ \not2} } \\ \tt U_n &= \tt 2 + 2(n - 1) + (n - 1)(n - 2) \\ \tt U_n &= \tt 2 + 2n - 2 + {n}^{2} - 2n - n + 2 \\ \tt U_n &= \bf{ \red{ {n}^{2} - n + 2}} \end{aligned} \: }\end{aligned} \\ \\

  • 2 suku berikutnya :

\begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_{n} &= \tt {n}^{2} - n + 2 \\ \tt U_{5} &= \tt {5}^{2} - 5 + 2 \\ \tt U_{5} &= \tt 25 - 5 + 2 \\ \tt U_{5} &= \tt 20 + 2 \\ \tt U_{5} &= \bf{ \red{22}} \\ \\ \tt U_{n} &= \tt {n}^{2} - n + 2 \\ \tt U_{6} &= \tt {6}^{2} - 6 + 2 \\ \tt U_{6} &= \tt 36 - 6 + 2 \\ \tt U_{6} &= \tt 30 + 2 \\ \tt U_{6} &= \bf{ \red{32}} \end{aligned} \: }\end{aligned}

------------------

\mathbb{ \color{red}{ \underbrace{KESIMPULAN}}}

Jadi, 2 suku berikutnya adalah 22 dan 32

\colorbox{ff0000}{} \colorbox{ff4000}{}\colorbox{ff8000}{}\colorbox{ffc000}{}\colorbox{ffff00}{}\colorbox{c0ff00}{}\colorbox{80ff00}{}\colorbox{40ff00}{}\colorbox{00ff00}{}\colorbox{00ff40}{}\colorbox{00ff80}{}\colorbox{00ffc0}{}\colorbox{00ffff}{}\colorbox{00c0ff}{}\colorbox{0080ff}{}\colorbox{0040ff}{}\colorbox{0000ff}{}\colorbox{4000ff}{}\colorbox{8000ff}{}\colorbox{c000ff}{}\colorbox{ff00ff}{}\colorbox{ff00c0}{}\colorbox{ff00a0}{}\colorbox{ff0080}{}\colorbox{ff0040}{}

[tex] \mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}[/tex]2, 4, 8, 14, 22, 32------------------[tex] \mathbb{ \color{orange}{ \underbrace{PENYELESAIAN}}}[/tex][tex] \small \boxed{ \begin{array}{c|c} \color{violet} \bf Rumus& \color{violet} \bf Keterangan \\ \hline & \tt{\color{red} U} {\color{lightgreen}_n} = suku \: ke - n ~~~~~~~~~~~\\ & \tt {\color{lightgreen}n} = banyak \: suku~~~~~~~~ \\ \boxed{ \: \color{orange} \tt {\color{red} U}{\color{lightgreen}_n} = {\color{magenta}a} + { \color{gold}b} ( {\color{lightgreen}n} - 1) + \small{ \frac{{ \color{aqua}c}({\color{lightgreen}n} - 1)({\color{lightgreen}n} - 2)}{2} } \: } &\tt {\color{magenta}a} = suku \: pertama~~~~~~ \\ & \tt { \color{gold}b} = beda \: (U_{2} - U_{1}) ~~~~~\\ & \tt {\color{aqua}c} = beda \: (tingkat \: 1) \end{array} } \\ \\[/tex][tex] \boxed{ \: \begin{aligned} &\tt {\bf2} \: \: \: 4 \: \: \: 8 \: \: \: 14 \: \: \: ... \begin{aligned} &\Rightarrow& \bf a = 2\end{aligned} \\ &\tt \: \: \: {\bf 2} \: \: \: 4 \: \: \: 6 \: \: \: ... \: \: \: \: \begin{aligned} &\Rightarrow& \bf b = 2\end{aligned} \\ & \: \: \: \: \: \: \tt{ \bf2} \: \: \: 2 \: \: \: ... \: \: \: \: \: \: \begin{aligned} &\Rightarrow& \bf \: c = 2\end{aligned} \end{aligned} \: } \\\\[/tex]rumus suku ke-n : [tex] \begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_n &= \tt a + b(n - 1) + \small{ \frac{c(n - 1)(n - 2)}{2}} \\ \tt U_n &= \tt 2 + 2(n - 1) + \small{ \frac{ \not2(n - 1)(n - 2)}{ \not2} } \\ \tt U_n &= \tt 2 + 2(n - 1) + (n - 1)(n - 2) \\ \tt U_n &= \tt 2 + 2n - 2 + {n}^{2} - 2n - n + 2 \\ \tt U_n &= \bf{ \red{ {n}^{2} - n + 2}} \end{aligned} \: }\end{aligned} \\ \\[/tex]2 suku berikutnya : [tex] \begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_{n} &= \tt {n}^{2} - n + 2 \\ \tt U_{5} &= \tt {5}^{2} - 5 + 2 \\ \tt U_{5} &= \tt 25 - 5 + 2 \\ \tt U_{5} &= \tt 20 + 2 \\ \tt U_{5} &= \bf{ \red{22}} \\ \\ \tt U_{n} &= \tt {n}^{2} - n + 2 \\ \tt U_{6} &= \tt {6}^{2} - 6 + 2 \\ \tt U_{6} &= \tt 36 - 6 + 2 \\ \tt U_{6} &= \tt 30 + 2 \\ \tt U_{6} &= \bf{ \red{32}} \end{aligned} \: }\end{aligned} [/tex]------------------[tex] \mathbb{ \color{red}{ \underbrace{KESIMPULAN}}}[/tex]Jadi, 2 suku berikutnya adalah 22 dan 32[tex] \colorbox{ff0000}{} \colorbox{ff4000}{}\colorbox{ff8000}{}\colorbox{ffc000}{}\colorbox{ffff00}{}\colorbox{c0ff00}{}\colorbox{80ff00}{}\colorbox{40ff00}{}\colorbox{00ff00}{}\colorbox{00ff40}{}\colorbox{00ff80}{}\colorbox{00ffc0}{}\colorbox{00ffff}{}\colorbox{00c0ff}{}\colorbox{0080ff}{}\colorbox{0040ff}{}\colorbox{0000ff}{}\colorbox{4000ff}{}\colorbox{8000ff}{}\colorbox{c000ff}{}\colorbox{ff00ff}{}\colorbox{ff00c0}{}\colorbox{ff00a0}{}\colorbox{ff0080}{}\colorbox{ff0040}{} [/tex]

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Last Update: Sun, 06 Nov 22
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