Question

Продолжите последовательность 1,16,81. Учи.ру

Answer 1

Последовательность по формуле
b(n) =n⁴
1⁴. 2⁴=16. 3⁴=81. 4⁴=256. 5⁴=625. 6⁴=1296 - ОТВЕТ

Answer 2

1,16,81,256,625,1296, 2401.

1-степень 1
16-степень 4
81-степень 9

между 1 и 4 d(разность)=3, между 4 и 5 d=5. Закономерность: d+2 каждую итерацию(повторение), следовательно, после 9 нужно возводить в квадрат 16, затем 25, затем 36, затем 49 и так далее.

Answer 3

Finding the Pattern in the Sequence 1, 16, 81

The given sequence is 1, 16, 81. To continue this sequence, we can look for a pattern or rule that governs the progression from one number to the next.

Upon examining the sequence, it appears that each number is a perfect square of the next odd number. In other words, each number is the square of the next consecutive odd number.

Therefore, to continue the sequence: - 1 is the square of 1 (1^2) - 16 is the square of 4 (4^2) - 81 is the square of 9 (9^2)

So, the next number in the sequence would be the square of the next consecutive odd number, which is 11. Therefore, the next number in the sequence is 121 (11^2).

This pattern follows the progression of perfect squares of consecutive odd numbers.

Conclusion

The sequence 1, 16, 81 follows the pattern of being the perfect squares of consecutive odd numbers, and the next number in the sequence is 121, which is the square of the next consecutive odd number, 11.