SOLUTION: Really confused!! Help is greatly appreciated. My question is;
The number 4,375 is which term of the arithmetic sequence a<sub>n</sub> = 3a<sub>n-1</sub>, if a<sub>1</sub> = 2.
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-> SOLUTION: Really confused!! Help is greatly appreciated. My question is;
The number 4,375 is which term of the arithmetic sequence a<sub>n</sub> = 3a<sub>n-1</sub>, if a<sub>1</sub> = 2.
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Question 767122: Really confused!! Help is greatly appreciated. My question is;
The number 4,375 is which term of the arithmetic sequence an = 3an-1, if a1 = 2.
a 7th term
b 8th term
c 9th term
d 6th term
In a, (n-1) is a lower exponent of a. and the 1 in a1 is another lower exponent to a. Its not above it like a normal exponent like 2^5, it's below it. please email me if you have any concerns! Answer by Edwin McCravy(20060) (Show Source):
an = 3an-1, if a1 = 2.
We check to see if it is a geometric sequence.
r =
Divide both sides of
an = 3an-1
by an-1,
= = = 3
and since r = , it is a geometric series with r = 3
an = a1rn-1
Substitute 4375 for an and 2 for a1
4375 = 2(3n-1)
Divide both sides by 2
2187.5 = 3n-1
Take logs of both sides"
log(2187.5) = log(3n-1)
log(2187.5) = (n-1)log(3)
= n-1
7.000208078 = n-1
8.000208-78 = n
That did not come out a whole number,
so the problem is botched. The 8th term is
an = a1rn-1
Substitute a1 = 2; n=8; r=3:
a8 = 2·38-1
a8 = 2·37
a8 = 4374
So you copied the problem wrong.
It should have been 4,374, not 4375.
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So change the problem from 4375 to 4374.
an = a1rn-1
Substitute 4374 for an and 2 for a1
4374 = 2(3n-1)
Divide both sides by 2
2187 = 3n-1
Take logs of both sides"
log(2187) = log(3n-1)
log(2187) = (n-1)log(3)
= n-1
7 = n-1
8 = n
So 4374 is the 8th term.
Edwin
