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The question can be answered using the arithmetic sequence formula: an = a1 + (n – 1)d.
d = 6
a1 = 9
n = 32
an = ?

an = 9 + (32-1)6
an = 9 + 31x6
an = 195

so, the 35th term is 195

Answer:

The thirty-second term of the sequence is:

                                 195

Step-by-step explanation:

We are given a sequence as:

       9,15, 21, .....

The first term of the sequence is:

\(a_1=a=9\)

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:

\(a=9\ and\ d=6\)

Also, we know that the nth term of a sequence is given by the formula:

\(a_n=a+(n-1)d\)

Hence,

\(a_{32}=9+(32-1)\times 6\\\\\\a_{32}=9+31\times 6\\\\\\a_{32}=9+186\\\\\\a_{32}=195\)

      Hence, the answer is:

               195

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