-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 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value