discover the next two numbers in series:?

Question

1. 1, 3,7,15,__,__
2. 2,12,36,80,150,___,___
3. 6,24,60,120,210,___,___
4. 18,22,22,20,26,___,___
5. 15,40,145,756,5089,___,___
6. 1,2,5,11,21,___,____
7. 1,4,12,22,34,___,___

if possible please show your solution... tnx.........

Answer 1

I'll give you some hints, but I won't answer them for you:
1) The difference between terms (2, 4, 8, ...)
2) 1, 4, 9, 16... and 1, 8, 27, 64...
3) 1!, 2!, 3!...
4) perhaps look at every other term...
5) n! and n^2
6) The difference between terms (1, 3, 6, 10, ... , 1+2+3+..+n)
7) Look at these as base 7 number (12 base 7 = 9, 22 base 7 = 16, etc.)

Answer 2

Just put in whatever two numbers you want. Then use LaGrange's interpolation polynomial [L(x)] to justify them using x as an integer index. That little trick used to get me thrown out of math classes in high school ☺

Or do what chads2k2 suggested ☺


Doug

Answer 3

Why not go ask your teacher how to do this, because this is CLEARLY a homework problem.

I just hope that people don't actually answer your homework problem, but I am sure they will.