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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 $a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}$ .

<h3>What is the missing element in a sequence?</h3>

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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8 0

2 years ago

An accounting firm has recently recruited six graduates: three men and three women. Three of the graduates are to be selected at

solong [7]

Answer:

a) The probability tree is constructed below

b) the probability that at least two women will be selected is 0.500

Step-by-step explanation:

Given the data in the question;

a) The probability tree is as follows;

3 men, 3 women

↓

_______________________|________________________

↓ ↓ ↓ ↓

3 men 2 men 1 man 0 men

0 women 1 woman 2 woman 3 women

b) the probability that at least two women will be selected

p( at least two women would be selected) = P( there are 2 women out of 3 ) + P( there 3 women out of 3

so

p( at least two women would be selected) = C

³C₂ × ³C₁ / ⁶C₃ + ³C₃³C₀ / ⁶C₃

= 3!/(2!(3-2)!) × 3!/(1!(3-1)!) / 6!/(3!(6-3)!) + 3!/(3!(3-3)!) × 3!/(0!(3-0)!) / 6!/3!(6-3)!)

= 3 × 3 / 20 + 1 × 1 / 20

= 9/20 + 1/20

= 0.45 + 0.05

p( at least two women would be selected) = 0.500

Therefore, the probability that at least two women will be selected is 0.500

6 0

3 years ago

Every Wednesday, Wayne works out for 3/4 of an hour at the fitness center. Every Saturday, he goes to the fitness center again a

matrenka [14]

3/4 of an hour = 45 minutes
45 * 3 = 135 minutes
135 + 45 = 180 minutes
He spends 180 minutes or 3 hours

4 0

2 years ago

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