Write a explicit formula for the sequence 10, 9.5, 9, 8.5, 8 then find ^a8

Explicit formula for the sequence is and

Step-by-step explanation:

Given: Sequence = 10, 9.5 , 9 , 8.5 , 8

To find: Explicit Formula for the sequence and 8th term of sequence

1st term of sequence = 10

2nd term of sequence = 9.5

3rd term of sequence = 9

4th term of sequence = 8.5

5th term of sequence = 8

Difference between 2nd and 1st term = 9.5 - 10 = -0.5

Difference between 3rd and 2nd term = 9 - 9.5 = -0.5

Since, Difference is same in both cases

⇒ It is Arthematic Progression

⇒ First term, a = 10 and Common term, d = -0.5

using formula of AP for nth term we get,

⇒ 8th Term of AP,

Therefore, Explicit formula for the sequence is and

Step-by-step explanation:

The given sequence is an arithmetic sequence, because each term can be found by applying a difference.

In this case, you can observe that such difference is -0.5, because each term is going down by 0.5 units.

The formula that describes an arithmetic sequence is

Where is the last term, is the first term, is the position of the last term and is the difference.

Each variable is

Where we are gonna find the term number eight. So, replacing values, we have

Therefore, the term number eight is 6.5.

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