Answer:
35
Explanation:
We know that the general formula for arithmetic sequence is
a_n=a_0+(n-1)d
Using the general formula, we can make equations for 6th term and 9th term
a_6=a_0+(6-1)d
a_6=a_0+5d
101=a_0+5d Eqn 1
For 9th term
a_9=a_0+(9-1)d
a_9=a_0+8d
83=a_0+5d Eqn 2
Subtracting equation 2 from equation 1
101-83=a_0+5d-(a_0+8d)
18=a_0+5d-a_0-8d
18=-3d
d= -6
Putting d=-6 in Eqn 1, we get:
101=a_0+5(-6)
101=a_0-30
a_0=101+30
a_0=131
Now that we have values of a_0, and d we can find the 17th term
a_17=a_0+(17-1)d
=131+(16)(-6)
=131-96
=35
So the 17th term is 35 ..