Answer:
503
Step-by-step explanation:
For an arithmetic sequence, the n-th term is found by
[tex]a_n = a_1 + (n - 1)d[/tex]
To find [tex]d[/tex] (the common difference) we can simply subtract one of the terms by the last, for example:
[tex]d = 299 - 305 \\d = -6 \\[/tex]
The common difference must be the same throughout the entire sequence, so we can do it once more just to be sure:
[tex]d = 305 - 311\\d = -6[/tex]
We also have to know that [tex]a_1[/tex] stands for the first term of the sequence, which in this case is 311.
Now that we know this, let's find the 32nd term
[tex]a_{32} = 311 + (32 - 1)-6\\a_{32} = 311 + 192\\a_{32} = 503[/tex]
Good luck!
