lenagonzalez84
Answered

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Find the sum of the geometric series for which a = 160, r = 0.5, and n = 6.

Sagot :

[tex]\\ \sf\longmapsto S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

[tex]\\ \sf\longmapsto S_n=\dfrac{160(1-0.5^6)}{1-0.5}[/tex]

[tex]\\ \sf\longmapsto S_n=\dfrac{160(1-0.015625)}{0.5}[/tex]

[tex]\\ \sf\longmapsto S_n=\dfrac{160(0.984378)}{0.5}[/tex]

[tex]\\ \sf\longmapsto S_n=80(0.984378)[/tex]

[tex]\\ \sf\longmapsto S_n=78.75[/tex]

Hi1315

Answer:

[tex]s _6 = 315[/tex]

Step-by-step explanation:

Here,

a = First term

r ,= common ratio

Now let's use this formula to find the sum of the above geometric series

[tex]s _n = \frac{a(1 - {r}^{n} )}{(1 - r)} \\ \\ s _6 = \frac{160(1 - {0.5}^{6} )}{(1 - 0.5)} \\ \\ s _6 = \frac{160 (1 - 0.015625)}{0.5} \\ \\ s _6 = \frac{157.5}{0.5} \\ \\ s _6 = 315[/tex]

Hope this helps you.

Let me know if you have any other questions:-)

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