Answer :
Answer:
The 32nd term of the arithmetic sequence is:
-372
Step-by-step explanation:
We are given first term of the sequence as:
[tex]a_1=-31[/tex]
We know that the nth term of a arithmetic sequence is given by the formula:
[tex]a_n=a_1+(n-1)d[/tex]
where d is the common difference of the arithmetic sequence.
We are given,
[tex]a_9=-119[/tex]
i.e.
[tex]a_1+(9-1)d=-119\\\\\\i.e.\\\\\\-31+8d=-119\\\\\\8d=-119+31\\\\\\8d=-88\\\\i.e.\\\\\\d=-11[/tex]
Hence, the 32nd term is given by:
[tex]a_{32}=-31+(32-1)\times (-11)\\\\\\a_{32}=-372[/tex]
Hence, the answer is: -372