What patterns do you notice? Share your observations and make conjectures. (Page 4)

Question

Bright Tutorials · Accepted Answer

In the above sequence, we notice that the sum of consecutive odd numbers is a perfect square.
We see that the next perfect square is the sum of the next consecutive odd number.
Observation:
1
2
= 1
2
2
= 1 + 3 = 4
3
2
= 1 + 3 + 5 = 9
4
2
= 1 + 3 + 5 + 7 = 16
5
2
= 16 + 9 = 25
6
2
= 25 + 11 = 36
7
2
= 36 + 13 = 49
.
.
.
.
28
2
= 729 + 55 = 784
29
2
= 784 + 57 = 841
30
2
= 841 + 59 = 900

A Square and A Cube — Question 2