Find the sum of the followinf series. Round to the nearest hundredth if necessary. 6+12+24+...+6144 Sum of a finite geometric series: S_n=frac{a_1-a_1r^n}{1-r}

opatovaL

opatovaL

Answered question

2021-01-06

Find the sum of the followinf series. Round to the nearest hundredth if necessary.
6+12+24++6144
Sum of a finite geometric series:
Sn=a1a1rn1r

Answer & Explanation

gwibdaithq

gwibdaithq

Skilled2021-01-07Added 84 answers

We have data: 
Series: 6+12+24++6144 
The series's average ratio is
r=a2a1 
Here, a1 is the first term of series and a2 is the second term of the series. 
Change the values in the equation above
r=126 
=2 
The series' concluding term is
L=a1rn1 
Change the values in the equation above
6144=6(2)n1 
2n1=1024 
2n1=210 
n1=10 
n=11 
The sum of finite geometric series is, 
Sn=a1a1rn1r 
Here, n is the number of terms in the series. 
Susbtitute the values in the above equation. 
Sn=66(2)1112 
Sn=66(2048)12 
Sn=122821 
=12282 
Consequently, a finite geometric series has a sum of 12282.

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