Tolong dooong,dikumpulin besok soalnya:(1. Rumus jumlah n suku pertama dari deret aritmatika 3+7+11+.... Question from @rizkypratiwi9914

September 2018 1 31 Report

Tolong dooong,dikumpulin besok soalnya:(
1. Rumus jumlah n suku pertama dari deret aritmatika 3+7+11+..... adalah ..
2. Jumlah n suku pertama deret aritmatika dirumuskan dengan Sn=7 $n^{2}$ + 5n. Suku ke 100 deret tersebut adalah....

IcukSugiarto $\bold{\underline{JAWABAN\ 1:}}\\deret\ aritmatika:3+7+11.....\\\\sehingga:\\a=3\\b=U_{2}-U_{1}\\~~=7-3=4\\\\maka\ untuk\ rumus\ jumlah\ n\ suku\ pertama:\\\boxed{S_{n}= \frac{n}{2}(2a+(n-1)b) }\\\boxed{S_{n}= \frac{n}{2}(2(3)+(n-1)(4)) }\\\boxed{S_{n}= \frac{n}{2}(6+4n-4) }$
$\boxed{S_{n}= \frac{n}{2}(4n+2) }\\\boxed{S_{n}= \frac{n(4n+2)}{2} }\\\boxed{S_{n}= \frac{2n(2n+1)}{2} }\\\boxed{S_{n}= n(2n+1) }\\atau:\\\boxed{S_{n}= 2n^{2}+n }$

$\bold{\underline{JAWABAN\ 2:}}$
$\bold{Note:}\\keterangan\ untuk\ penyelesaian\ cara\ cepat:\\p=7\\q=5\\n=100$

$\bold{Pilihlah\ dari\ ketiga\ model\ jawaban\ yg\ mudah\ di\ pahami :)}$

$\bold{\underline{\bigstar~~Smart\ Solution:}}\\U_{n} = S_{1} + (n-1) 2p\\U_{100} = (7+5) + (100-1) 2(7)\\U_{100} = 12 + (99) 14\\U_{100} = 12 + 1386\\U_{100} = 1398$

$\bold{\underline{\bigstar~~Smart\ Solution\ Version\ 2:}}\\U_{n} = 2pn + (q-p)\\U_{100} = 2(7)(100) + (5-7)\\U_{100} = 1400 + (-2)\\U_{100} = 1398$

$\bold{\underline{\bigstar~~General\ Solution:}}\\S_{n} = 7n^{2}+ 5n\\Sehingga:\\U_{n} = S_{n}- S_{n-1}\\U_{100} = S_{100}- S_{100-1}\\U_{100} = S_{100}- S_{99}\\U_{100} = (7(100)^{2}+ 5(100))-(7(99)^{2}+ 5(99))\\U_{100} = (7(10000)+ 5(100))-(7(9801)+ 5(99))\\U_{100} = (70000+ 500)-(68607+ 495)\\U_{100} = 70500 -69102\\U_{100} = 1398$

$\bold{\underline{\bigstar~icuk18sugiarto~\bigstar~}}$

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