SOLUTION: find the common ratio, the first term, and an explicit formula for the nth term. Given a2=3 and a8=192

Question 860691: find the common ratio, the first term, and an explicit formula for the nth term. Given a2=3 and a8=192
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
arithmetic sequence
an = a + (n - 1)d
192 = a + 7d,
3= a + 2d
189=5d
d=37.8
a = -363/5, d = 189/5
a=-72.600, d=37.800
an = -363/5 + (n - 1)*189/5
geometric sequence
Tn = t * r^(n - 1)
192 = t * r^7,
3 = t * r^2
r = 2*2^(1/5), t = 3/(4 2^(2/5))
Tn = 3/(4 2^(2/5)) * 2*2^(1/5)^(n - 1)

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