Question 1154055
<font color=black size=3>
There are 2 ways to do this kind of problem. 


The first method involves listing out 35 terms, each new term is found by subtracting 5 from the previous term (eg: -39 - 5 = -44, or -44-5 = -49, and so on). This is not recommended because there are so many terms. It's easy to lose track. 


A much better method is to use the general nth term formula of an arithmetic sequence. That formula is
{{{a[n] = a[1] + d(n-1)}}}
The first term is {{{a[1] = -39}}}. The common difference is {{{d = -5}}} since we add on -5 each time, or subtract 5 each time, to get the next term. 


So,
{{{a[n] = a[1] + d(n-1)}}} 


{{{a[n] = -39 + (-5)(n-1)}}} 


{{{a[n] = -39-5n+5}}} 


{{{a[n] = -5n-34}}}


--------------------------------------------------------


As a check, let's plug in a random positive integer between 1 and 4 to see if it matches up with the proper element in the sequence we're given. I'll do n = 3 
{{{a[n] = -5n-34}}} 


{{{a[3] = -5(3)-34}}} Replace n with 3


{{{a[3] = -15-34}}} 


{{{a[3] = -49}}} 


The third term is <font color=blue>-49</font>


Sure enough, the third term of the given sequence {-39, -44, <font color=blue>-49</font>, -54, ...} is <font color=blue>-49</font>. I'll let you check the other values of n (1, 2 and 4) to see if things line up properly or not.


--------------------------------------------------------


Once we know the nth term formula, we plug in n = 35 to get the 35th term of the arithmetic sequence
{{{a[n] = -5n-34}}} 


{{{a[35] = -5(35)-34}}} Replace n with 35


{{{a[35] = -175-34}}} 


{{{a[35] = -209}}} 


The 35th term is <font size=4 color=red>-209</font>
</font>