Question

Which equation could be used to calculate the sum of the geometric series? one-third two-ninths startfraction 4 over 27 endfraction startfraction 8 over 81 endfraction startfraction 16 over 243 endfraction

Answer 1

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

Sum of geometric sequence

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