diketahui barisan bilangan 2,6,12,20 Tentukan tiga suku berikutnya.... Question from @uniw79110

uniw79110 @uniw79110

September 2022 1 10 Report

diketahui barisan bilangan 2,6,12,20 Tentukan tiga suku berikutnya

Gusti2601

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

2, 6, 12, 20, 30, 42, 56

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

$\small \boxed{ \beginno numeric noise key 1235no numeric noise key 1234 \colorno numeric noise key 1233 \bf rumus& 1232 keterangan \\ \hline & \tt{\colorno numeric noise key 1231 u} {\colorno numeric noise key 1230_n} =suku \: ke - n ~~~~~~~~~~~\\ \tt 1229n} =banyak suku~~~~~~~~ 1228 1227 u}{\colorno numeric noise key 1226_n} ={\colorNO NUMERIC NOISE KEY 1225a} + { 1224b} ( 1223n} 1) \small{ \frac{{ 1222c}({\colorno numeric noise key 1221n} 1)({\colorno numeric noise key 1220n} 2)}no numeric noise key 1219 } &\tt 1218a} =suku pertama~~~~~~ 1217b} =beda (u_no numeric noise key 1216 u_no numeric noise key 1215) ~~~~~\\ 1214c} =beda (tingkat \endno numeric noise key 1213 \\$

$\boxed{ \: \beginno numeric noise key 1204 &\tt {\bf2} 6 12 20 ... 1203 &\rightarrow& \bf a =2\endNO NUMERIC NOISE KEY 1202 \\ {\bf 4} 8 1201 b =4\endNO NUMERIC NOISE KEY 1200 & \tt{ \bf2} 2 ...\: 1199 c =2\endNO NUMERIC NOISE KEY 1198 \endno numeric noise key 1197 } \\\\$

rumus suku ke-n :

$\beginno numeric noise key 1185& \implies& \boxed{ \: 1184 \tt u_n & =\tt a + b(n - 1) \small{ \fracno numeric noise key 1183no numeric noise key 1182} \\ 2 4(n \frac{ \not2(n 1)(n 2)}{ \not2} } (n 2) 4n 4 no numeric noise key 1181^no numeric noise key 1180 2n n \tt{ 1179^no numeric noise key 1178 n} \bf{ \redno numeric noise key 1177} \endno numeric noise key 1176 }\endno numeric noise key 1175 \\$

tiga suku berikutnya :

$\begin{aligned}& \implies& \boxed{ \: \begin{aligned} \tt U_n &= \tt {n(n + 1)} \\ \tt U_{5} &= \tt 5(5 + 1) \\ \tt U_{5} &= \tt 5(6) \\ \tt U_{5} &= \bf{ \red{30}} \\ \\ \tt U_{n} &= \tt n(n + 1) \\ \tt U_{6} &= \tt 6(6 + 1) \\ \tt U_{6} &= \tt 6(7) \\ \tt U_{6} &= \bf{ \red{ 42}} \\ \\ \tt U_{n} &= \tt n(n + 1) \\ \tt U_{7} &= \tt 7(7 + 1) \\ \tt U_{7} &= \tt 7(8) \\ \tt U_{7} &= \bf{ \red{56}} \end{aligned} \: }\end{aligned}$

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

Jadi, 3 suku berikutnya adalah 30, 42, 56

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

Gusti2601 JAWABAN :
\mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}

Gusti2601 warna-warni :

Gusti2601 \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}{}

Gusti2601 RUMUS :
\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}

Gusti2601 \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} }

Gusti2601 \tt {\color{red} U} .....// yang rumus tidak bisa dikirim, jadi saya kirim terpisah

Gusti2601 iya, sama² ^^