-8,-8,-6,-2,4,12,22 quadratic sequence

9514 1404 393

  a[n] = n^2 -3n -6

Step-by-step explanation:

First differences are ...

  -8 -(-8) = 0

  -6 -(-8) = 2

  -2 -(-6) = 4

Second differences are ...

  2 -0 = 2

  4 -2 = 2

Constant second differences indicate a degree 2 (quadratic) sequence.

The general formulation can be written as ...

  an = a1 +(n -1)(d1 +(n -2)/2(d2)) . . . . where a1 is the first term; d1 is the first first difference; d2 is the second difference

  = -8 +(n -1)(0 +(n -2)/2(2)) = -8 +(n -1)(n -2)

  an = n^2 -3n -6 . . . . . formula for the n-th term

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

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