Question

write an algebraic expression that describes this sequence: 0,6,16,30. thanks!

Answer 1

0 when n = 0

*** 6

6 ***** 4

*** 10

16 **** 4

*** 14

30 when n = 3

ah ha, change of change is constant
Of form y = a + b n + c n^2
a = 0 because first term is 0
so of form
y = b n + c n^2
when n = 1, y = 6
6 = b (1) + c (1)
when n = 2, y = 16
16 = b(2) + c (4)
so solve for b and c
12 = 2 b + 2 c
16 = 2 b + 4 c
---------------
- 4 = -2 c
c = 2
then
6 = b + 2 so b = 4
so
y = 4 n + 2 n^2
check
if n = 3
y = 12 + 18 = 30 yes

Answer 2

Write an expression that is equivalent to -15.66 ÷ 5.8. Then, find the quotient.