Pyramid Investigations 2 – Consecutive Number Pyramids

Refer to the solution of this problem which suggests that $1+2+3+..+(n-1)+n+(n-1)+...+3+2+1=n^2$ .

Using that we can say ----->

$1+2+3+4+5+4+3+2+1 = 5^2 = \boxed{25}$

always mid term square here 5 so 5 square is equal to 25

if we see , the sequence is 1^2,2^2,3^2,4^2,5^2.Therefore, 1,4,9,16 ,25.

5^5=25

1+2+3+4+5+4+3+2+1=25

Here is a seris...

1^2=1

2^2=4

3^2=9

4^2=16

5^2=25

If we are on term four, then the number is just h^2 = 16. So the next term is h^2 + 2h + 1, or (h + 1)^2 = 25

Square the no.of Items in the Center of the Pyramid.

1+2+1= 2^{2}=4 1+2+3+2+1=3^{2}=9 1+2+3+4+3+2+1=4^{2}=16 there fore, 1+2+3+4+5+4+3+2+1=5^{2}=25

1+2+3+4+5+4+3+2+1 = (1+4)+(2+3)+(5)+(4+1)+(3+2) = 5+5+5+5+ 5 = 5*5 = 25

ans can be find out by the maximum value in the question and just square it . in our question max. value is 5 after squaring it .we get 25 as our answer alternatively just add those values given in the question as 1+2+3+4+5+4+3+2+1=25.

look at the number exactly at the middle of patterns. (easiest,fastest way to think) 1+2+3+4+5+4+3+2+1 5 is the exactly middle number. Now, just square it. 5^2
you get the answer 25.

Applying formula NXN that is maximum number is 5X5 =25 Ans K.K.GARG.India

if the middle term is n then use ( ) n times and add two in every term as ( 1)+(1+2)+(1+2+2)+(1+2+2+2)+(1+2+2+2+2) no of 2 in nth term will be (n-1) answer is 25

terribly easy...should have been a challenge!

Just add the numbers up! 2(1+2+3+4)+5=25

n(n+1)/2+(n-1)n/2 = (n^2+n+n^2-n)/2 = n^2, here n=5 so result is 25

n(n+1)/2 + n(n-1)/2 =n^2