i have the question
The counting numbers are written in the pattern at the righ. Find the midle number of the 40th row.
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16 [/LEFT]
solution is 1561.
simple method is to make general term of the middle element of each row using A.P then finding the 40th element
general term will be n(n-1)+1
n=1 gives 1
n=2 gives 3
n=3 gives 7
these all are middle term of each row so on putting 40 middle number of 40th row will be obtained
Hello, rai2003!
. . . . . .
The middle numbers form this sequence: .
Take the differences of consecutive terms,
. . then the differences of the differences and so on.
. .
Since the second differences are constant,
. . the generating function is of the second degree . . . a quadratic.
The general quadratic function is: .
We know the first term terms of the sequence.
. .
Substitute into [4]: .
Substitute into [1]: .
Hence, the generatng function is: .
Therefore: .