Answer:
1. 7
2. 3
3. 9
Step-by-step explanation:
Answer:
increasing sequence of +7
Step-by-step explanation:
please mark brainiest
please give 5 stars
thank you
850/630= 1.35 exchange rate
150x1.35= 202.50
Answer:
![a_n=2+3n](https://tex.z-dn.net/?f=a_n%3D2%2B3n)
![\displaystyle S_n=\frac{7n+3n^2}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_n%3D%5Cfrac%7B7n%2B3n%5E2%7D%7B2%7D)
Step-by-step explanation:
<u>Arithmetic Sequences
</u>
The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
![a_n=a_1+(n-1)r](https://tex.z-dn.net/?f=a_n%3Da_1%2B%28n-1%29r)
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
The sum of the n terms of an arithmetic sequence is given by:
![\displaystyle S_n=\frac{a_1+a_n}{2}\cdot n](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_n%3D%5Cfrac%7Ba_1%2Ba_n%7D%7B2%7D%5Ccdot%20n)
We are given the first two terms of the sequence:
a1=5, a2=8. The common difference is:
r = 8 - 5 = 3
Thus the general term of the sequence is:
![a_n=5+(n-1)3=5+3n-3=2+3n](https://tex.z-dn.net/?f=a_n%3D5%2B%28n-1%293%3D5%2B3n-3%3D2%2B3n)
![\boxed{a_n=2+3n}](https://tex.z-dn.net/?f=%5Cboxed%7Ba_n%3D2%2B3n%7D)
The formula for the sum is:
![\displaystyle S_n=\frac{5+2+3n}{2}\cdot n](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_n%3D%5Cfrac%7B5%2B2%2B3n%7D%7B2%7D%5Ccdot%20n)
![\displaystyle S_n=\frac{7+3n}{2}\cdot n](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_n%3D%5Cfrac%7B7%2B3n%7D%7B2%7D%5Ccdot%20n)
Operating:
![\boxed{\displaystyle S_n=\frac{7n+3n^2}{2}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdisplaystyle%20S_n%3D%5Cfrac%7B7n%2B3n%5E2%7D%7B2%7D%7D)