Posted by **Anonymous** on Sunday, November 11, 2012 at 2:30pm.

What are the missing numbers in this sequence?

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

- math -
**Reiny**, Sunday, November 11, 2012 at 5:37pm
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) = **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

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