Verified Answer :
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:
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
\(a_{1} =10\\d=-0.5\ =8\\\)
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.