Question

What is the missing pattern 7, 11, 2, 18, -7

Answer 1

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula $n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}$, equivalent to the recurrence formula $a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}$.

What is the missing element in a sequence?

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

$n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}$      (1)

Now we prove that given expression contains the pattern:

n = 0

7

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula $n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}$, equivalent to the recurrence formula $a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}$.

To learn more on patterns: brainly.com/question/23136125

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