Question

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

Answer 1

Answer:

Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

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,

$a_n=a+(n-1)d$

$a_n=10+(n-1)(-0.5)$

$a_n=10-0.5n+0.5$

$a_n=10.5-0.5n$

⇒ 8th Term of AP, $a_8=10.5-0.5\times8=10-4=6$

Therefore, Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

Answer 2

Answer:

The term number eight is 6.5

$a_{8}=6.5$

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

$a_{n}=a_{1}+(n-1)d$

Where $a_{n}$ is the last term, $a_{1}$ is the first term, $n$ is the position of the last term and $d$ is the difference.

Each variable is

$a_{1} =10\\d=-0.5\\n=8$

Where we are gonna find $a_{8}$ the term number eight. So, replacing values, we have

$a_{n}=a_{1}+(n-1)d\\a_{8}=10+(8-1)(-0.5)\\a_{8}=10+7(-0.5)=10-3.5\\a_{8}=6.5$

Therefore, the term number eight is 6.5.