Given:
The sequence is:
![-3,5,13,21...](https://tex.z-dn.net/?f=-3%2C5%2C13%2C21...)
To find:
The explicit formula for the given sequence then find the 47th term.
Solution:
We have,
![-3,5,13,21...](https://tex.z-dn.net/?f=-3%2C5%2C13%2C21...)
The difference between two consecutive terms are:
![5-(-3)=8](https://tex.z-dn.net/?f=5-%28-3%29%3D8)
![13-5=8](https://tex.z-dn.net/?f=13-5%3D8)
![21-13=8](https://tex.z-dn.net/?f=21-13%3D8)
The given sequence has a common difference. So, the given sequence is an arithmetic sequence with first term -3 and common difference 8.
The explicit formula for an arithmetic sequence is:
![a_n=a+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d)
Where, a is the first term and d is the common difference.
Putting
and
in the above formula, we get
![a_n=-3+(n-1)8](https://tex.z-dn.net/?f=a_n%3D-3%2B%28n-1%298)
![a_n=-3+8n-8](https://tex.z-dn.net/?f=a_n%3D-3%2B8n-8)
![a_n=8n-11](https://tex.z-dn.net/?f=a_n%3D8n-11)
Putting
, we get
![a_{47}=8(47)-11](https://tex.z-dn.net/?f=a_%7B47%7D%3D8%2847%29-11)
![a_{47}=376-11](https://tex.z-dn.net/?f=a_%7B47%7D%3D376-11)
![a_{47}=365](https://tex.z-dn.net/?f=a_%7B47%7D%3D365)
Therefore, the explicit formula for the given sequence is
and the 47th term is 365.
Step-by-step explanation:
take the picture and attach with this file
Answer:
The answer is C jazz, opera and rock 12+10+18 = 40
Step-by-step explanation:
Answer:
How far is it from his grandparents house
Hi! This might be long but I hope it helps!
1. 115. If q=4, then the equation tells us that 0.1d+(0.25)⋅4=12.5. Subtracting 1 from both sides gives 0.1d=11.5, so d=115.
2. 100. If q=10, then the equation tells us that 0.1d+(0.25)⋅10=12.5. Subtracting 2.5 from both sides gives 0.1d=10, so d=100.
3. Yes. If you know the number of quarters, then you can determine the number of dimes from the equation. We can even write the equation in a way that shows this: d=125−2.5q. The expression 125−2.5qrepresents the output—it is the rule that determines the output d from a given input q.