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Serggg [28]
2 years ago
14

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

Mathematics
2 answers:
harina [27]2 years ago
6 0

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

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

\\ \sf\longmapsto S_n=\dfrac{160(1-0.015625)}{0.5}

\\ \sf\longmapsto S_n=\dfrac{160(0.984378)}{0.5}

\\ \sf\longmapsto S_n=80(0.984378)

\\ \sf\longmapsto S_n=78.75

Crazy boy [7]2 years ago
6 0

Answer:

s _6 = 315

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

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

Hope this helps you.

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

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