Diketahui barisan bilangan 2,7,12,17,...tentukan:A) rumus ke-NB) Suku ke 55 barisan

Berikut ini adalah pertanyaan dari jgfuufiufcufxgugc pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

Diketahui barisan bilangan 2,7,12,17,...tentukan:
A) rumus ke-N
B) Suku ke 55 barisan tersebut

Diketahui barisan bilangan 5,11,19,29,...
A) rumus ke-N
B) suku ke 20 barisan tersebut

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

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

SOAL 1 :

$\begin{aligned}&&&& \sf a.&&\begin{aligned} \boxed{ \: \bf U_{n} = 5n - 3 \: } \end{aligned} \end{aligned}$

$\begin{aligned}&&&& \sf b.&&\begin{aligned} \boxed{ \: \bf U_{55} = 272 \: } \end{aligned} \end{aligned}$

SOAL 2 :

$\begin{aligned}&&&& \sf a.&&\begin{aligned} \boxed{ \: \bf U_{n} = {n}^{2} + 3n + 1 \: } \end{aligned} \end{aligned}$

$\begin{aligned}&&&& \sf b.&&\begin{aligned} \boxed{ \: \bf U_{20} = 461 \: } \end{aligned} \end{aligned}$

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

SOAL 1 :

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

$\boxed{ \: \begin{aligned} &\tt {\bf2} \: \: \: 7 \: \: \: 12 \: \: \: 17 \: \: \: ... \begin{aligned} &\Rightarrow& \bf a = 2\end{aligned} \\ &\tt \: \: \: {\bf 5} \: \: \: \: 5 \: \: \: \: 5 \: \: \: ... \: \: \: \: \: \begin{aligned} &\Rightarrow& \bf b = 5\end{aligned} \end{aligned} \: } \\ \\$

rumus suku ke-n :

$\begin{aligned} &\implies& \boxed{ \: \begin{aligned} \tt U_{n} &= \tt a + (n - 1)b \\ \tt U_{n} &= \tt 2 + (n - 1)5 \\ \tt U_{n} &= \tt 2 + 5n - 5 \\ \tt U_{n} &= \bf \red{5n - 3} \end{aligned} \: } \end{aligned} \\ \\$

suku ke 55 :

$\begin{aligned} &\implies& \boxed{ \: \begin{aligned} \tt U_{n} &= \tt{5n - 3} \\ \tt U_{55} &= \tt5(55) - 3 \\ \tt U_{55} &= \tt275 - 3 \\ \tt U_{55} &= \bf{ \red{272}} \end{aligned} \: } \end{aligned} \\ \\$

$___________________________________________$

$\\$

SOAL 2 :

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

$\boxed{ \: \begin{aligned} &\tt {\bf5} \: \: \: 11 \: \: \: 19 \: \: \: 29 \: \: \: ... \begin{aligned} &\Rightarrow& \bf a = 5\end{aligned} \\ &\tt \: \: \: {\bf 6} \: \: \: \: \: 8 \: \: \: \: 10 \: \: \: ... \: \: \: \: \begin{aligned} &\Rightarrow& \bf b = 6\end{aligned} \\ & \: \: \: \: \: \: \tt{ \bf2} \: \: \: \: \: \: 2 \: \: \: ...\: \: \: \: \: \: \: \: \: \begin{aligned} &\Rightarrow& \bf c \: = 2\end{aligned} \end{aligned} \: } \\\\$

rumus suku ke-n :

$\begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_n &= \tt a + b(n - 1) + \small{ \frac{c(n - 1)(n - 2)}{2}} \\ \tt U_n &= \tt 5 + 6(n - 1) + \small{ \frac{ \not2(n - 1)(n - 2)}{ \not2} } \\ \tt U_n &= \tt 5 + 6(n - 1) + (n - 1)(n - 2) \\ \tt U_n &= \tt 5 + 6n - 6 + {n}^{2} - 2n - n + 2 \\ \tt U_n &= \bf \red{ {n}^{2} + 3n + 1} \end{aligned} \: }\end{aligned} \\ \\$

suku ke 20 :

$\begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_n &= \tt {n}^{2} + 3n + 1 \\ \tt U_{20} &= \tt {20}^{2} + 3(20) + 1 \\ \tt U_{20} &= \tt 400 + 60 + 1 \\ \tt U_{20} &= \bf \red{461} \end{aligned} \: }\end{aligned}$

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