math
posted by Anonymous on .
What are the missing numbers in this sequence?
1.25, 3.5, 8, 17, 35, 71, ___, ___, 575,...

If you make a difference table, you will see that
they are:
1.25, 4.5 , 9 , 18 , 36
starting at the second the difference is twice the previous difference
e.g t5 = t4 + 2(t4  t3) = 3t4  2t3
in general
t(n+1) = 3t(n)  2t(n1) , n> 2, t(1) = 1.25 , t(2) = 3.5
so
t(7) = 3t(6)  2t(5) = 3(71)2(35) = 143
t(8) = 3t(7)  2t(6) = 3(143)  2(71) = 287
check:
t(9) = 3t(8) 2t(7) = 3(287)  2(143 = 575 , YEAHHH