Write a rule for the nth term of the geometric sequence and then find a_5 given a_4=189/1000,r=3/5

miniliv4 2022-10-03 Answered
Write a rule for the nth term of the geometric sequence and then find a 5 given a 4 = 189 1000 , r = 3 5
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Answers (1)

Mario Monroe
Answered 2022-10-04 Author has 12 answers
We know we can write every geometric sequence in the form of below:
a n = a 1 × r n - 1
and for now what we have to do is to figure out what is our first term ( a 1 ) and we can do it easily cause we have a 4 :
a 4 = 189 1000 = a 1 × ( 3 5 ) 3
and we have to solve this equation for a 1
a 1 = 189 1000 3 3 5 3 = 189 × 125 1000 × 27 = 7 8
Now we can rewrite our equation for any nth term:
a n = a 1 × r n - 1 = 7 8 × ( 3 5 ) n - 1
and we can calculate a 5 just by putting our n=5 in the equation.
a 5 = 7 8 × ( 3 5 ) 4 = 567 500
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