# Question:Fibonacci 1. Here are the first 5 terms of a quadratic sequence.1371321Find an expression, in terms of n for the nth term of this quadratic sequence.

9514 1404 393

n² -n +1

Step-by-step explanation:

First differences of the terms of the sequence are ...

3-1 = 2

7-3 = 4

13-7 = 6

21-13 = 8

Second differences are ...

4-2 = 2

6-4 = 2

8-6 = 2

In a quadratic sequence the coefficient of the squared term is half of the second difference value. Here, that means the squared term will be (2/2)n² = n².

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We can find the other terms of the quadratic expression by considering the differences between n² and the actual sequence.

The sequence of n² terms is ...

1, 4, 9, 16, 25

When we subtract these from the actual sequence, we get ...

1-1 = 0

3-4 = -1

7-9 = -2

13-16 = -3

21-25 = -4

That is, the amount subtracted from n² is one less than the term number.

The expression for the n-th term is ...

an = n² -n +1

## Related Questions

Raghav has to load 2456 cartons of apples equally in 5 trucks. how many cartons will be left unloaded in the end?​

12,280

Step-by-step explanation:

just do 1456×5 :))

A certain firm has plants a, b, and c producing respectively 35\%, 15\%, and 50\% of the total output. The probabilities of a nondefective product are, respectively, 0.75, 0.95, and 0.85. A customer receives a defective product. What is the probability that it came from plant c?

The proportion of production that is defective and from plant A is

... 0.35·0.25 = 0.0875

The proportion of production that is defective and from plant B is

... 0.15·0.05 = 0.0075

The proportion of production that is defective and from plant C is

... 0.50·0.15 = 0.075

Thus, the proportion of defective product that is from plant C is

... 0.075/(0.0875 +0.0075 +0.075) = 75/170 = 15/34 ≈ 44.12%

_____

P(C | defective) = P(C&defective)/P(defective)

The question required the use of Bayes' theorem to determine the probability of a defective product coming from plant c. Given the probabilities of defectiveness for each plant, the calculation indicated that there is approximately a 54.55% chance that a defective product came from plant c.

### Explanation:

The problem described can be solved using Bayes' theorem, which is a principle in Probability that is used when we need to revise/or update the probabilities of events given new data. Since a defective product is received, and we need to determine the probability of it coming from plant c, we apply Bayes' theorem for the probability of events a, b, and c (representative of the products from the respective plants).

The Bayesian formula we will use, given the probabilities of a, b and c respectively and the probability of receiving a nondefective product from these plants, is: P(c|defective) = [P(defective|c) * P(c)] / [P(defective|a) * P(a) + P(defective|b) * P(b) + P(defective|c) * P(c)].

First, calculate the probability of a defective product from each plant (1 minus the probability of a nondefective product): these are 0.25 for plant a, 0.05 for plant b, and 0.15 for plant c.

Then substitute the values: P(c|defective) = [0.15 * 0.50] / [(0.25 * 0.35) + (0.05 * 0.15) + (0.15 * 0.5)] = 0.075 / 0.1375 = 0.5454545.

So, given a defective product, there is approximately a 54.55% chance that it was produced by plant c.

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What's the range of this function graph​

[2,∞)

Step-by-step explanation:

The range is the y intercept and the function starts at 2 and continues going up causing the range of the function to be [2,∞)

A = 1 −7 −1 2 , B = 3 7 −1 0 , C = 1 0 −1 1 Find: a) BC, b) 5A − 2C, c) A + C,

b

Step-by-step explanation:

Ac and bd are perpendicular bisectors of each other. adc. Find eab

Ac and BD are perpendicular bisectors of each other ⇒⇒ (Given information)

∴ BD

∵∠DEA = 90°    ⇒⇒⇒ from the given information
∴∠DAE = 90° - β

And AC bisects ∠DAB
⇒⇒⇒ from the given information
∴∠EAB = ∠DAE = 90° - β

<EAB = 180 - 90 - (0.5*<ADC)

Cuánto le falta a 3/5para llegar a 9/10