SOLUTION: URGENT QUESTION... the question is- if a sequence follows the same pattern as a, ar, ar^2... and t4=8 and t7=1 find a, r, and t10 thanks

Question 207864: URGENT QUESTION...
the question is-
if a sequence follows the same pattern as a, ar, ar^2... and t4=8 and t7=1
find a, r, and t10
thanks
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
geometric sequence ,,,t(n) = a(1) r^(n-1)
.
given,,,t(4) =a r^(4-1) =ar^3 =8
.
given,,,t(7) =ar^(7-1) = ar^6 =1
.
(ar^6 =1)/(ar^3 = 8)
.
r^(6-3) =1/8
.
r^3 = 1/8,,,,take cube root
.
r= .5 ,,,,,answer
.
subst,,,,ar^3=8,,,,a*(.5)^3 =8,,,,,a=64,,,,answer
.
check,,,,ar^3=8,,,,,(64)* .5^3 = 8,,,,,,ok
.
ar^6=1,,,,,,(64)*.5^6 =1,,,,,ok
.
to find t(10) =ar^(10-1) =ar^9 =(64)*.5^9 = .125 = 1/8,,,answer

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