The image shows a sequence of numbers: 6, -11, 22, -44, 88, -132. We need to identify the pattern and find the next number in the sequence.

1. Problem Description

The image shows a sequence of numbers: 6, -11, 22, -44, 88, -

1

3

2. We need to identify the pattern and find the next number in the sequence.

2. Solution Steps

Let's analyze the given sequence: 6, -11, 22, -44, 88, -

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3

2.

* Observe the absolute values: 6, 11, 22, 44, 88, 132

* Let's analyze the ratio between consecutive terms. The ratios between the absolute values of the terms are not constant. This suggests we cannot determine the closed-form formula with ratio between each term. The pattern of the sign is alternating.

Let's analyze the difference between consecutive terms.

$-11-6 = -17$

$22 - (-11) = 33$

$-44 - 22 = -66$

$88 - (-44) = 132$

$-132 - 88 = -220$

The differences do not seem to have a pattern. Therefore we should look at the ratios.

Dividing each term by its predecessor, we have the ratios:

$\frac{-11}{6} = -1.8333$

$\frac{22}{-11} = -2$

$\frac{-44}{22} = -2$

$\frac{88}{-44} = -2$

$\frac{-132}{88} = -1.5$

The numbers have alternating signs. Moreover, from the second number onward it's roughly multiplying by -

2. Let's analyze the series based on this information. Notice that each value in the sequence is roughly the previous value times -

2. If the previous value is 88, the next value is roughly -

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7

6. However the listed values do not meet this criterion. It's likely to be alternating multiply by the factor of 2 or close to

2.

Let us consider the absolute value of difference between the terms, the difference between values are not linear.

If we multiply each previous number by -2, we will get -12, 22, -44, 88, -

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7

6.

Let's re-examine the sequence: 6, -11, 22, -44, 88, -

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2. Note that from the second term onward, terms alternate signs. Also, if we ignore the first term 6, the terms are -11, 22, -44, 88, -132 where each of these values can be obtained by multiplying by -2 and then modifying them by some value.

Let the terms be $a_1, a_2, a_3, a_4, a_5, a_6 ...$.

$a_1 = 6$.

$a_2 = -11 = a_1 * -2 + 1$.

$a_3 = 22 = a_2 * -2 + 0$.

$a_4 = -44 = a_3 * -2 + 0$.

$a_5 = 88 = a_4 * -2 + 0$.

$a_6 = -132 = a_5 * -1.5$.

This pattern does not help us find the next number.

Consider the sequence of absolute values 11, 22, 44, 88, 132...

Taking the differences: 11, 22, 44

Then, 22 - 11 = 11; 44 - 22 =

2

2. Let's say the next difference will be

4

4. Therefore 132 + 44 =

1

7

6. Therefore, the next term in the sequence can be 176*(-1) = -

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7

6.

3. Final Answer

-176