Answer:
The first term is 14
The common difference is -2.5
Step-by-step explanation:
we know that
The rule to calculate the an term in an arithmetic sequence is

where
d is the common difference
a_1 is the first term
we have that
The third term of an arithmetic sequence is equal to 9
so


substitute

----> equation A
The rule to find the sum of the the first n terms of the arithmetic sequence is equal to
![S=\frac{n}{2} [2a_1+(n-1)d]](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Bn%7D%7B2%7D%20%5B2a_1%2B%28n-1%29d%5D)
we have
The sum of the first 8 term is 42
so


substitute
![42=\frac{8}{2} [2a_1+(8-1)d]](https://tex.z-dn.net/?f=42%3D%5Cfrac%7B8%7D%7B2%7D%20%5B2a_1%2B%288-1%29d%5D)
![42=4[2a_1+7d]](https://tex.z-dn.net/?f=42%3D4%5B2a_1%2B7d%5D)
----> equation B
Solve the system of equations
----> equation A
----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
the solution is (14,-2.5)
see the attached figure
therefore

The first term is 14
The common difference is -2.5
Answer:
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Step-by-step explanation: