Enter the first 4 terms of the sequence defined by the rule given.

f(n) = n2/2

YES

Step-by-step explanation:

Explicit rules for arithmetic sequences follow the format

a

n

=

d

(

n

−

1

)

+

a

1

(or with a

f

(

n

)

instead of an

a

n

), where

d

represents the common difference and

a

1

represents the first term

To find the first 4 terms, plug

1

,

2

,

3

,

4

in for

n

:

f

(

1

)

=

7

(

1

−

1

)

−

10

f

(

1

)

=

7

(

0

)

−

10

f

(

1

)

=

0

−

10

f

(

1

)

=

−

10

Do the same thing for

2

,

3

,

4

The first four terms are

−

10

,

−

3

,

4

,

11

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).