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masha68 [24]
2 years ago
9

Which equation could be used to calculate the sum of the geometric series? one-third two-ninths startfraction 4 over 27 endfract

ion startfraction 8 over 81 endfraction startfraction 16 over 243 endfraction
Mathematics
1 answer:
Andrew [12]2 years ago
3 0

The equation could be used to calculate the sum of the geometric series is S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }

<h3>Sum of geometric sequence</h3>

Geometric sequence are sequence that increase expoentially. The formula for calculating the sum of an exponential sequence is expressed as:

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

where

  • a is the first term
  • n is the number of terms
  • r is the common ratio

From the given sequence

a= 1/3

r = 2/9 * 3 = 2/3

Substitute into the formula

S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }

Hence the equation could be used to calculate the sum of the geometric series is S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }

Learn more on geometric series here; brainly.com/question/24643676

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