tolong pakek cara kerja yaa
[tex] \mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}[/tex]
C. 342
------------------
[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 {\bf30} \: \: \: 42 \: \: \: 56 \: \: \: 72 \: \: \: 90 \: \: \: ... \begin{aligned} &\Rightarrow& \bf a = 30\end{aligned} \\ &\tt \: \: \: \: {\bf 12} \: \: \: 14 \: \: \: 16 \: \: \: 18 \: \: \: ... \: \: \: \: \begin{aligned} &\Rightarrow& \bf b = 12\end{aligned} \\ & \: \: \: \: \: \: \: \: \: \tt{ \bf2} \: \: \: \: \: \: 2 \: \: \: \: \: \: 2 \: \: \: ... \: \: \: \: \: \: \: \: \begin{aligned} &\Rightarrow& \bf \: c = 2\end{aligned} \end{aligned} \: } \\\\[/tex]
- rumus suku ke-n
[tex] \boxed{ \: \begin{aligned} \tt{U_{n}} &= \tt{a + b(n - 1) + \small{ \frac{c(n - 1)(n - 2)}{2} }} \\ \tt{U_{n}} &= \tt{30 + 12(n - 1) + \small{ \frac{ \not{2}(n - 1)(n - 2)}{ \not{2}} }} \\ \tt{U_{n}} &= \tt{}30 + 12n - 12 + (n - 1)(n - 2) \\ \tt{U_{n}} &= \tt{}30 + 12n - 12 + {n}^{2} - 2n - n + 2 \\ \tt{U_{n}} &= \tt{ {n}^{2} + 9n + 20} \\ \tt{U_{n}} &= \tt{}(n + 4)(n + 5) \end{aligned} \: } \\ \\ [/tex]
- suku ke 14
[tex] \boxed{ \: \begin{aligned} \tt{U_{n}} &= \tt{(n + 4)(n + 5)} \\ \tt{U_{14}} &= \tt{(14 + 4)(14 + 5)} \\ \tt{U_{14}} &= \tt{(18)(19)} \\ \tt{U_{14}} &= \red{ \boxed{ \green{ \bf{342}}}} \end{aligned} \: }[/tex]
------------------
[tex] \mathbb{ \color{red}{ \underbrace{KESIMPULAN}}}[/tex]
Jadi, suku ke 14 dari barisan tersebut adalah 342
[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]
