The first term of an infinite geometric sequence is 18, while the third term is 8. There are two possible sequences. Find the sum of each sequence.
Answers
Answer:
S1=54, S2=54/5=10.8
Step-by-step explanation:
a=18
ar^2=8
=>18*r^2=8
r^2=8/18=4/9
r=+-(2/3)
Sequence 1 (r=+2/3):- 18,12,8,16/3...…..
S1=a/(1-r)=18/(1-2/3)=54
Sequence 2 (r=-2/3):- 18,-12,8,-16/3...…..
S2=a/(1-r)=18/[1-(-2/3)]=18/(1+2/3)=54/5=10.8
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Given : The first term of an infinite geometric sequence is 18, while the third term is 8.
There are two possible sequences.
To Find : the sum of each sequence.
Solution:
a = 18
ar² = 8
=> r² = 8/18
=> r² = 4/9
=> r = ±2/3
First sequence
a = 18 , r = 2/3
Sum = a /(1 - r)
= 18/(1 - 2/3)
= 54
Second sequence
a = 18 r = - 2/3
18/(1 - (-2/3)) = 54/5 = 10.8
or it can be converted in 2 sequence
one with
a = 18 and r = 4/9 and another a = - 12 and r = 4/9
Sum = 18/(1 - 4/9) - 12/(1 - 4/9)
= 6 * 9/5
= 54.5
= 10.8
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