The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
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:
[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex] (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 [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
To learn more on patterns: https://brainly.com/question/23136125
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