Question

What is the nth term rule of the linear sequence below? 15 , 7 , − 1 , − 9 , − 17 , . . .

Answer 1

You can see that you're constantly subtracting 8 to get the next number. So, we have

$a_1 = 15$

$a_2 = a_1-8$

$a_3 = a_2-8 = (a_1-8)-8=a_1-2\cdot 8$

$a_4=a_1-3\cdot 8$

$a_5=a_1-4\cdot 8$

So, as you can see, to get the n-th term we must subtract (n-1) times 8 from the original number.