Diketahui deret geometri 2 + 4 + 8 + 16 +.... Tentukan jumlah enam suku pertama deret geometri tersebut!

M u lt i pl y 1 7 2 ​ t im es p e nni es in ja r 1 7 2 ​ ∗ 133 = 7 9 ​ ∗ 133 = 7 1197 ​ = 171 I n t h e bi gg er ja r t h ere a re 171 p e nni es .

Answered by luana | 2024-06-10

The bigger jar contains 171 pennies. This is calculated by multiplying 1 7 2 ​ by the 133 pennies in the smaller jar. The final calculation shows that there are 171 pennies in total in the bigger jar.
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Answered by luana | 2024-10-02

Pola deret geometri = 2 + 4 + 8 + 16 + ....Suku pertama (a) = [tex]U_{1} = 2[/tex]Rasio (r) = [tex]\frac{U_{2}}{U_{1}} = \frac{4}{2} = 2[/tex]Rumus suku ke-n [tex](U_{n})[/tex] adalah[tex]U_{n} = a \times {r}^{n - 1} [/tex][tex]U_{n} = 2 \times {2}^{n - 1} [/tex][tex]U_{n} = {2}^{1 + (n - 1)} [/tex][tex]U_{n} = {2}^{1 + n - 1} [/tex][tex]U_{n} = {2}^{n + 1 - 1} [/tex][tex]U_{n} = {2}^{n + 0} [/tex][tex]U_{n} = {2}^{n} [/tex]Jadi, jumlah 6 suku pertama deret tersebut adalah[tex]S_{n} = \frac{a \: ({r}^{n} - 1)}{r - 1} [/tex][tex]S_{6} = \frac{2 \: ({2}^{6} - 1)}{2 - 1} [/tex][tex]S_{6} = \frac{2 \: (64 - 1)}{2 - 1} [/tex][tex]S_{6} = \frac{2 \: (63)}{1} [/tex][tex]S_{6} = \frac{126}{1} [/tex][tex]S_{6} = 126[/tex]

Answered by MaulanaAlief | 2025-07-19