Question

Find the thirty-second term of the following sequence.

9, 15, 21, ...
186
199
195

Answer 1

The thirty-second term of the sequence is:

195

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)* 6\\\\\\a_(32)=9+31* 6\\\\\\a_(32)=9+186\\\\\\a_(32)=195`

Hence, the answer is:

195

Answer 2

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