ANSWER
The 35th term is -8
EXPLANATION
The nth term of an arithmetic sequence is given by
[tex]a_n = a_1 + d( n - 1)[/tex]
We have the 17th term to be;
[tex]a_{17}=47[/tex]
and the common difference is d=-3
We substitute to get:
[tex]47= a_1 + - 3(1 7- 1)[/tex]
[tex]47= a_1 + 16( - 3)[/tex]
[tex]47= a_1 - 48[/tex]
[tex]a_1 = 48 + 47 = 95[/tex]
We can now find the 35th term:
[tex]a_{35}=a_{1} + 34d[/tex]
[tex]a_{35}=95 + 34( - 3) = - 8[/tex]
