Question

What are the missing numbers in this sequence?

1.25, 3.5, 8, 17, 35, 71, ___, ___, 575,...

Answer 1

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(n-1) , n> 2, t(1) = 1.25 , t(2) = 3.5

so
t(7) = 3t(6) - 2t(5) = 3(71)-2(35) = <b>143</b>
t(8) = 3t(7) - 2t(6) = 3(143) - 2(71) = <b>287</b>

check:
t(9) = 3t(8) -2t(7) = 3(287) - 2(143 = <b>575</b> , YEAHHH