Find the sum of the finite geometric series. Round to the nearest hundredth. $\sum _ { n = 1 } ^ { 6 } \left( - \frac { 8 } { 9 } \right) ^ { n }$
A) $- 0.24$
B) $- 0.10$
C) $- 0.33$
D) $- 0.80$
E) $- 0.63$

Question

Quizplus · Accepted Answer

The sum of the finite geometric series is given by the formula:$$S_n = \frac{a(1-r^n)}{1-r}$$where a is the first term, r is the common ratio, and n is the number of terms.In this case, a = -8/9, r = -8/9, and n = 6. Substituting these values into the formula, we get:$$S_6 = \frac{-8/9(1-(-8/9)^6)}{1-(-8/9)}$$$$S_6 = \frac{-8/9(1-(-0.583)^6)}{1-(-8/9)}$$$$S_6 = \frac{-8/9(1-0.000001)}{1-(-8/9)}$$$$S_6 = \frac{-8/9(0.999999)}{1/9}$$$$S_6 = -0.239999$$Rounding to the nearest hundredth, we get -0.24.

Find the Sum of the Finite Geometric Series ∑n=16(−89)n\sum _ { n = 1 } ^ { 6 } \left( - \frac { 8 } { 9 } \right) ^ { n }∑n=16​(−98​)n

Find the Sum of the Finite Geometric Series $\sum _ { n = 1 } ^ { 6 } \left( - \frac { 8 } { 9 } \right) ^ { n }$