Question

Продолжи ряд 3\5,6\22, 9/39,12/56

Answer 1

15/74, 18/93, 21/113

Answer 2

To find a pattern and continue the given sequence, let's observe the numerators and denominators separately:

Numerator sequence: 3, 6, 9, 12, ... Denominator sequence: 5, 22, 39, 56, ...

To find a relationship between the two sequences, let's look at the differences between consecutive terms:

Numerator differences: 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3, ... Denominator differences: 22 - 5 = 17, 39 - 22 = 17, 56 - 39 = 17, ...

The numerator differences are constant (3), and the denominator differences are also constant (17). This suggests that there is a linear relationship between the numerators and denominators.

Now, to find the next terms in the sequence, we can add the constant differences to the last terms:

The last numerator is 12, and the constant difference is 3, so the next numerator will be 12 + 3 = 15. The last denominator is 56, and the constant difference is 17, so the next denominator will be 56 + 17 = 73.

Therefore, the next term in the sequence is 15/73.

The continued sequence is: 3/5, 6/22, 9/39, 12/56, 15/73, ...