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Dmitry_Shevchenko [17]
2 years ago
5

The common ratio in a geometric series is 0.5 and the first term is 256.

Mathematics
1 answer:
Anastaziya [24]2 years ago
5 0

Answer:

504

Step-by-step explanation:

Given,

common ratio (r) = 0.5

first term (a_1) is 256

Sum of first n terms in geometric series is given by the formula (r < 1):

S_n=\frac{a(1-r^n)}{1-r}

Hence, sum of first 6 terms mean:

r = 0.5

a = 256

n = 6

Substituting, we get the answer to be:

S_n=\frac{a(1-r^n)}{1-r}\\S_6=\frac{256(1-(0.5)^6)}{1-0.5}\\S_6=504

The sum of first 6 terms is 504

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