1. Dua suku berikutnya dari barisan 243, 81, 27, 9, 3, ... adalah ....2. Rumus suku ke-n pada barisa.... Question from @hafizahnoviyanti44

August 2022 1 4 Report

1. Dua suku berikutnya dari barisan 243, 81, 27, 9, 3, ... adalah ....
2. Rumus suku ke-n pada barisan 56, 49, 42, 35, ... adalah .....
3. Suku ke-10 dari barisan 2, 5, 8, 11, 14, ... adalah ....
tolong bantu jawab ya bsk pagi mau dikumpulin

Gusti2601

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

1 dan ⅓
63 - 7n
29

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

SOAL 1 :

$\boxed{ \begin{array}{c|c} \color{violet} \bf Rumus& \color{violet} \bf Keterangan \\ \hline & \tt{\color{magenta} U} \blue{_n} = suku \: ke - n ~~~~~\\ \boxed{ \: \tt {\color{magenta} U} \color{aqua} \blue{_n} = \purple {a} \cdot \green{r}^{ \blue{n} - 1} \: } & \tt \purple{a} = suku \: pertama \\ & \tt \green{r} = rasio \: \left( \frac{U_{2}}{U_{1}} \right) ~~~\end{array} } \\ \\$

$\boxed{ \: \begin{aligned} &\tt{a = \purple{243}} \\ &\tt{r = \frac{81}{243} = \green{ \frac{1}{3} }} \end{aligned} \: } \\ \\$

rumus suku ke-n

$\boxed{ \: \begin{aligned} \tt{U_n} &= \tt{ \purple{a} \cdot { \green{r}}^{n - 1} } \\ \tt{U_n} &= \tt{ \purple{243} \cdot {\left( \green{ \frac{1}{3}} \right)}}^{n - 1} \\ \tt{U_n} &= \tt{ {3}^{5} \cdot {\left( \frac{1}{ {3}^{1} } \right)}^{n - 1} } \\ \tt{U_n} &= \tt{ {3}^{5} \cdot {\left( {3}^{ - 1} \right)} }^{n - 1} \\ \tt{U_n} &= \tt{ {3}^{5} \cdot {3}^{ - n + 1} } \\ \tt{U_n} &= \tt{ {3}^{5 + ( - n) + 1} } \\ \tt{U_n} &= \pink{\tt{ {3}^{6 - n} }} \end{aligned} \:}&\begin{aligned}&\begin{aligned} \red{ \bf{ingat : }}\end{aligned} \\ &\boxed{ \: \begin{aligned} \tt{{a}^{ - n}} &= \tt{ \frac{1}{ {a}^{n} } } \\ \tt{ {( {a}^{m} )}^{n} } &= \tt{ {a}^{m \times n} } \\ \tt{ {a}^{m} \times {a}^{n} } &= \tt{ {a}^{m + n} } \end{aligned} \: }\end{aligned} \\ \\$

dua suku berikutnya (U6 dan U7)

$\boxed{ \: \begin{array}{c|c} \begin{aligned} \tt{U_{n}} &= \tt{ {3}^{6 - n} } \\ \tt{U_{6}} &= \tt{ {3}^{6 - 6} } \\ \tt{U_{6}} &= \tt{ {3}^{0} } \\ \tt{U_{6}} &= \red{ \boxed{ \pink{ \bf{{1}}}}} \\ \\ \\ \end{aligned}& \begin{aligned} \tt{U_{n}} &= \tt{ {3}^{6 - n} } \\ \tt{U_{7}} &= \tt{ {3}^{6 - 7} } \\ \tt{U_{7}} &= \tt{ {3}^{ - 1} }\\ \tt{U_{7}} &= \small{ \tt{ \frac{1}{ {3}^{1} }}}\\ \tt{U_{7}} &= \small{ \red{ \boxed{ \bf{ \pink{ \frac{1}{3} }}}}} \end{aligned} \end{array} \: }& \begin{aligned} &\begin{aligned} \red{ \bf{ingat : }} \end{aligned} \\ &\boxed{ \: \begin{aligned} \tt{ {a}^{0} } &= \tt{1} \\ \tt{ {a}^{ - n} } &= \tt{ \frac{1}{ {a}^{n} } } \end{aligned} \: } \end{aligned}\\ \\$

SOAL 2 :

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

$\boxed{ \: \begin{aligned} &\tt{a = \purple{56}} \\ &\tt{b = 49 - 56 = \orange{ ( - 7)}} \end{aligned} \: } \\ \\$

rumus suku ke-n

$\boxed{ \: \begin{aligned}\tt{U_{n}} &= \tt{ \purple{a} + (n - 1) \orange{b}} \\ \tt{U_{n}} &= \tt{ \purple{56} + (n - 1) \orange{( - 7)}} \\ \tt{U_{n}} &= \tt{ \purple{56} - 7n + 7} \\ \tt{U_{n}} &= \red{ \boxed{ \pink{ \tt{63 - 7n}}}} \end{aligned} \: } \\ \\$

SOAL 3 :

$\boxed{ \: \begin{aligned} &\tt{a = \purple{2}} \\ &\tt{b = 5 - 2 = \orange{3}} \\ &\tt{n = \blue{10}} \end{aligned} \: } \\ \\$

suku ke-10

$\boxed{ \: \begin{aligned}\tt{U_{n}} &= \tt{ \purple{a} + ( \blue{n} - 1) \orange{b}} \\ \tt{U_{10}} &= \tt{ \purple{2} + ( \blue{10} - 1) \orange{3}} \\ \tt{U_{10}} &= \tt{ \purple{2} + (9) \orange{3}} \\ \tt{U_{10}} &= \tt{ \purple{2} + 27} \\ \tt{U_{10}}&= \red{ \boxed{ \bf{ \pink{29}}}} \end{aligned} \: }$

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