The thirty-second term of the sequence is:
195
We are given a sequence as:
9,15, 21, .....
The first term of the sequence is:
[tex]a_1=a=9[/tex]
Also, we could observe that the sequence has a common difference(d) : 6
Since,
15-9=6
21-15=6
This means that the sequence is an arithmetic sequence with:
[tex]a=9\ and\ d=6[/tex]
Also, we know that the nth term of a sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]
Hence,
[tex]a_{32}=9+(32-1)\times 6\\\\\\a_{32}=9+31\times 6\\\\\\a_{32}=9+186\\\\\\a_{32}=195[/tex]
Hence, the answer is:
195
