Notice that the above sequence is arithmetic because the common difference: d is constant.
d = second term - first term.
= 15 - 9
= 6
The general term of an arithmetic sequence is,
a_{n} =a_{1} +(n-1)d
Where , nth term = [tex] a_{n} [/tex]
[tex] a_{1} [/tex] = First term
and d = common difference.
The given sequence is: 9, 15, 21, ...
Here a_{1} = 9,
d = 6
We need to find the 31st term. So, n = 31.
Next step is to plug in these values in the above formula. Therefore,
[tex] a_{31} =9 +(31-1)*6 [/tex]
= 9 + 30* 6
= 9 + 180
= 189
So, 31st term of this sequence is 189.
Hope this helps you.
