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Afina-wow [57]
2 years ago
15

For each of the following sequences, • Give a formula for the nth term in the sequence, • Give a recursive definition for the se

quence (ie. initial values and a recursive equation). (a) 1, 2, 3, 4, 5, . . . (b) 1, 2, 4, 8, 16, 32, . . . (c) 1, 2, 6, 24, 120, . . .
Mathematics
1 answer:
Andrew [12]2 years ago
5 0

Answer:

(a)n^{th} = n

f(1) = 1

f(n) = f(n-1) + 1

(b)n^{th} = 2^{n-1}

f(1) = 1

f(n) = f(n-1) * 2

(c)n^{th} = n!

f(1) = 1

f(n) = f(n-1) * n

Step-by-step explanation:

(a) This is a sequence of consecutive number

n^{th} = n

f(1) = 1

f(n) = f(n-1) + 1

(b) This is a sequence of 2 to the power of n - 1. The next number is twice time of this number

n^{th} = 2^{n-1}

f(1) = 1

f(n) = f(n-1) * 2

(c) This is factorial sequence. Where the next number is this number multiplied by n^{th}

n^{th} = n!

f(1) = 1

f(n) = f(n-1) * n

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OleMash [197]

Answer:

The solution is x=3 , y=-4 or (3,-4)

Step-by-step explanation:

Given equations (1 and 2) are:

3x- 2y = 17\\-2x -5y = 14

To solve a system of equation with elimination method, the co-efficients of one of the variables has to be equated and then the equations are added or subtracted to get an equation in one variable.

Multiplying equation 1 by 2:

2(3x-2y) = 2*17\\6x-4y = 34\ \ \ \ \ Eqn\ 3

Multiplying equation 2 by 3

3(-2x-5y) = 3*14\\-6x-15y = 42\ \ \ \ Eqn\ 4

Adding equation 3 and 4

(6x-4y) + (-6x-15y) = 34+42\\6x-4y-6x-15y = 76\\-19y = 76\\\frac{-19y}{-19} = \frac{76}{-19}\\y = -4\\

Putting y = -4 in equation 1

3x-2(-4) = 17\\3x+8 = 17\\3x = 17-8\\3x = 9\\\frac{3x}{3} = \frac{9}{3}\\x = 3

Hence,

The solution is x=3 , y=-4 or (3,-4)

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2 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Add all of the numbers together then divide by the amount of numbers there are.

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