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notka56 [123]
2 years ago
13

First four terms f(n)=n^3-n^2+1

Mathematics
2 answers:
g100num [7]2 years ago
5 0

Answer:

1, 5, 19, 49

Step-by-step explanation:

To obtain the first 4 terms substitute n = 1, 2, 3, 4 into f(n)

f(1) = 1³ - 1² + 1 = 1 - 1 + 1 = 1

f(2) = 2³ - 2² + 1 = 8 - 4 + 1 = 4 + 1 = 5

f(3) = 3³ - 3² + 1 = 27 - 9 + 1 = 18 + 1 = 19

f(4) = 4³ - 4² + 1 = 64 - 16 + 1 = 48 + 1 = 49

The first 4 terms are 1, 5, 19, 49

mrs_skeptik [129]2 years ago
3 0

Answer:

The function of this equation is: F(n)=\frac{1}{4}n^4-\frac{1}{3}n^3+n+C

Step-by-step explanation:

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Find the 4th term (x-y)^12
maria [59]

Answer:

The fourth term of the expansion is -220 * x^9 * y^3

Step-by-step explanation:

Question:

Find the fourth term in (x-y)^12

Solution:

Notation: "n choose k", or combination of k objects from n objects,

C(n,k) = n! / ( k! (n-k)! )

For example, C(12,4) = 12! / (4! 8!) = 495

Using the binomial expansion formula

(a+b)^n

= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n

For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is

C(n,3)a^(n-3)b^3

=C(12,3) * x^(12-3) * (-y)^(3)

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3 0
3 years ago
The sum of three numbers is 24. Twice the middle number is 2 more than the largest number, and the largest number is equal to th
harina [27]

Answer:

  • x = 5, y = 7, z = 12

Step-by-step explanation:

<u>Let the numbers be x, y and z</u>

  • x + y + z = 24
  • 2y = z + 2
  • z = x + y

<u>Solving by substitution:</u>

  • x + y + z = z + z = 24
  • 2z = 24
  • z = 12

  • 2y = z + 2
  • 2y = 12 + 2
  • 2y = 14
  • y = 7

  • z = x + y
  • x = z - y
  • x = 12 - 7 = 5

<u>The answer:</u>

  • x = 5, y = 7, z = 12
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Answer:

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