Let starting term, a = 9
Also let a = [tex] t_{1} [/tex]
So, [tex] t_{1} [/tex] = 9
[tex] t_{2} [/tex] = 15
[tex] t_{3} [/tex] = 21
[tex] t_{2} [/tex] - [tex] t_{1} [/tex] = 6
[tex] t_{3} [/tex] - [tex] t_{2} [/tex] = 6
∴ this is an arithmetic sequence.
We need to formulate a rule of the form:
[tex] t_{n} [/tex] = a + (n - 1)d
where n = the [tex] n^{th} [/tex] term
So, let n = 32
[tex] t_{32} [/tex] = 9 + (32 - 1)6
= 9 + 31 x 6
= 9 + 186
= 195
If I have calculated correctly, the 32nd term shoud be 195.
