Next three terms rule of 36, 49, 64, 81, .....
the differences are 13,15,17, ...
all the numbers are squared
6^2=36
7^2=49
8^2=64
9^2=81
10^2=100
so on
To find the next three terms in the given sequence, we need to identify the pattern or rule that governs the sequence.
From the given sequence: 36, 49, 64, 81, ...
We can observe that each term is a perfect square of a number.
Starting with 36, the square root of 36 is 6. The next perfect square after 36 is 49, whose square root is 7. Similarly, the next perfect square is 64 with a square root of 8, and the next perfect square is 81 with a square root of 9.
So, the pattern or rule governing the sequence is that each term is the square of the next consecutive whole number.
Using this pattern, we can find the next three terms:
The next number is the square of the next whole number, which is 100 (10^2), since the next whole number is 10.
Therefore, the next term in the sequence is 100.
Following the same pattern, the next two terms in the sequence will be the squares of the subsequent whole numbers:
The term after 100 will be the square of the next whole number, which is 121 (11^2).
The term after 121 will be the square of the next whole number, which is 144 (12^2).
So, the next three terms in the sequence are 100, 121, 144.