Question

Дан ряд чисел 2, 6, 12, 20, 30, 42, 56... Найти число, которое находится на 2006 месте​

Answer 1

Ответ:

на 2006 месте 4010

Answer 2

Finding the Number at the 2006th Position in the Given Sequence

To find the number at the 2006th position in the given sequence, let's analyze the pattern of the sequence.

The given sequence is: 2, 6, 12, 20, 30, 42, 56...

Looking at the sequence, we can observe that each number is obtained by adding the next odd number to the previous number. For example, to get from 2 to 6, we add 4 (the next odd number). To get from 6 to 12, we add 6 (the next odd number), and so on.

To find the number at the 2006th position, we need to determine the sum of the first 2005 odd numbers and add it to the first number in the sequence, which is 2.

To calculate the sum of the first 2005 odd numbers, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

In this case, the first term is 1 (the first odd number) and the last term is 2005 (the 2005th odd number).

Let's calculate the sum:

Sum = (2005/2)(1 + 2005) = 1002 * 2006 = 2,011,212

Now, we add this sum to the first number in the sequence:

Number at the 2006th position = 2 + 2,011,212 = 2,011,214

Therefore, the number at the 2006th position in the given sequence is 2,011,214.