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
we have
The sum of the first 8 term is 42
so
substitute
----> 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
