Question

3,6,12,24,48... 1,-2,3,-4... Надо найти формулу помогитеее

Answer 1

В 1 задании———
все постепеные цифры умножаются на 2 то есть 3•2=6,6•2=12 и так далее


во 2 задании———
все числа прибавляются на 1 то есть после -4идет 5,после5 идет -6 потом 7 и так далее………

Answer 2

Arithmetic Sequence: 3, 6, 12, 24, 48...

The given sequence is an arithmetic sequence, where each term is obtained by adding a constant difference to the previous term. To find the formula for this sequence, we need to determine the common difference.

Let's calculate the differences between consecutive terms:

- The difference between 6 and 3 is 6 - 3 = 3. - The difference between 12 and 6 is 12 - 6 = 6. - The difference between 24 and 12 is 24 - 12 = 12. - The difference between 48 and 24 is 48 - 24 = 24.

From these differences, we can observe that the common difference is increasing by a factor of 2 each time. Therefore, the common difference for this sequence is 3, 6, 12, 24, ...

To find the formula for the nth term of an arithmetic sequence, we can use the formula:

nth term = first term + (n - 1) * common difference

In this case, the first term is 3 and the common difference is increasing by a factor of 2 each time. So the formula for the nth term of this sequence is:

nth term = 3 + (n - 1) * 2

Let's verify this formula using the given terms:

- For n = 1, the formula gives us: 3 + (1 - 1) * 2 = 3, which is the first term. - For n = 2, the formula gives us: 3 + (2 - 1) * 2 = 5, which is the second term. - For n = 3, the formula gives us: 3 + (3 - 1) * 2 = 7, which is the third term. - For n = 4, the formula gives us: 3 + (4 - 1) * 2 = 9, which is the fourth term.

The formula seems to be working correctly for the given terms.

Pattern: 1, -2, 3, -4...

The given sequence does not follow a simple arithmetic or geometric pattern. However, we can observe that the signs alternate between positive and negative, and the absolute values of the terms increase by 1 each time.

To find a formula for this sequence, we can use the following pattern:

- For odd values of n, the term is n. - For even values of n, the term is -n.

Let's verify this pattern using the given terms:

- For n = 1, the pattern gives us: 1, which is the first term. - For n = 2, the pattern gives us: -2, which is the second term. - For n = 3, the pattern gives us: 3, which is the third term. - For n = 4, the pattern gives us: -4, which is the fourth term.

The pattern seems to be working correctly for the given terms.

Therefore, the formula for the nth term of this sequence is:

nth term = (-1)^(n+1) * n

Let's verify this formula using a few more terms:

- For n = 5, the formula gives us: (-1)^(5+1) * 5 = -5, which is the fifth term. - For n = 6, the formula gives us: (-1)^(6+1) * 6 = 6, which is the sixth term.

The formula seems to be working correctly for the given terms.

I hope this helps! Let me know if you have any further questions.