Complete the recursive rule and the explicit rule for the arithmetic sequence. 84, 94, 104, 114, 124, The recursive rule is f(1) = , f(n) = f(n − 1) + for n ≥ 2. The explicit rule is f(n) = + (n − 1).

Given:

The arithmetic sequence is

84, 94, 104, 114, 124,....

To find:

The recursive rule and the explicit rule for the arithmetic sequence.

Solution:

We have, the arithmetic sequence

84, 94, 104, 114, 124,....

Here,

First term : a=84

Common difference : d=94-84=10

The recursive rule for an arithmetic sequence is

So, the recursive rule for the given arithmetic sequence is

where, f(1)=84 and n ≥ 2.

Explicit rule for the arithmetic sequence is

So, the explicit rule for the given arithmetic sequence is

where, n ≥ 1.

Therefore, the recursive and explicit rules are and respectively.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

answer: 4 meters

step-by-step explanation: to you understand 2/3 better you can do 1 divided by 3 = . then multiply that by the 2 which is .66666666666666667 then you would do 6 x .66666666666666667 which is 4.      

hope this .