Question

+&g226+2+-+-+3 94. Use the formula to evaluate the seriesRound your answer to the nearest hundredth.S, =a1(1 - 1)1-In the formula for a finite series, ay is the first term, r is the common ratio, and n is the number of terms.9.0128.998.97

Answer 1

This geometric progression is given by 6 + 2 + 2/3 + 2/9 + ... + a6

We can calculate common ratio r with any two terms a_n and a_n+1 as follows:

`r=(a_(n+1))/(a_n)`

With the terms a1 = 6 ans a2 = 2 we have r = 2/6 = 1/3

Therefore, we have:

`S_6=(a_1(1-r^6))/(1-r)=(6\cdot(1-(1/3)^6))/(1-1/3)=8.99`