Please show us what you have tried and exactly where you are stuck.Can somebody help me in finding the pattern of the sum of the diagonal?
I noticed the bottom right number is a square number
Thank you for your help
View attachment 33772
If the bottom-right number is x^2, then the first # of the sequence is "x' (the number in the top right corner),yes sir, I have tried it, I work out that the number in the bottom right is a square number, but I am having problems finding the total of the diagonal.
How do i start finding the equation of the total of the diagonal, that's what i am stuck with
This is a problem in recognizing patterns. There are two ways to discover possible patterns. One is to experiment, meaning try things. The other way is try to figure out what patterns may make sense. Or you can try both.yes sir, I have tried it, I work out that the number in the bottom right is a square number, but I am having problems finding the total of the diagonal.
How do i start finding the equation of the total of the diagonal, that's what i am stuck with
I realised that for n X n table, the number in the bottom left would be x + (n-1)(x-1) and equate it with 5335, where x is the top-right number and n is the sequence, but i end up with 2 variables?If the bottom-right number is x^2, then the first # of the sequence is "x' (the number in the top right corner),
the second # is [x +(x-1)],
the third # is ?
Can you write the whole sequence in terms of 'x'?
How do 'x' & 'n' depend on each other?I realised that for n X n table, the number in the bottom left would be x + (n-1)(x-1) and equate it with 5335, where x is the top-right number and n is the sequence, but i end up with 2 variables?
What does x represent? We cannot help you if you do not say what things mean.I realised that for n X n table, the number in the bottom left would be x + (n-1)(x-1) and equate it with 5335, where x is the top-right number and n is the sequence, but i end up with 2 variables?
Hint: Sum of squares of n natural numbers | [n(n+1)(2n+1)] / 6 |
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The sum S = x + [x+(x-1)] + [x + 2*(x-1)] +[x+3*(x-1)} .... + [x + (x-1)(x-1)] = x*x +(x-1)*[1+2+...(x-1)] = x^2 + (x-1)*x*(x-1)/2 = (x^3 + x) / 2Can somebody help me in finding the pattern of the sum of the diagonal?
I noticed the bottom right number is a square number
Thank you for your help
View attachment 33772
n2−n+1=5335. solving for n, then squaring it, would also give me the answer for the bottom right value is it?The sum S = x + [x+(x-1)] + [x + 2*(x-1)] +[x+3*(x-1)} .... + [x + (x-1)(x-1)] = x*x +(x-1)*[1+2+...(x-1)] = x^2 + (x-1)*x*(x-1)/2
where the bottom-right-corner number of the table is x^2
Check
For the given table x = 6 and S = 36 + 25*3 = 111
Sum of diagonal numbers = 6 + 11 + 16 + 21 + 26 + 31 = 111 .................... checks
That is incorrect - read the response #11 and #12.n2−n+1=5335. solving for n, then squaring it, would also give me the answer for the bottom right value is it?
i focused on that, and now somebody said it's wrong, i am getting more lost, can somebody explain why?That is incorrect - read the response #11 and #12.
I am lost in the take first differences. no joySince I messed up so badly, let me give a far more detailed hint
If n = 1, the relevant sum is 1.
If n = 2, the relevant sum is 5
If n = 3, the relevant sum is is 15
If n = 4, the relevant sum is 34.
If n = 5, the relevant sum is 65
If n = 6, the relevant sum is 111
Take first differences. No joy.
Take second differences. No joy.
Take third differences. Looks like a cubic.
Do you know how to find it using the three first differences?
I truly apologize for getting off track in my second post