Question

Explicit formula for an, the nth term of the sequence 6, 0, -6, ....

Answer 1

This is an arithmetic sequence with first term 6 and common difference -6
Nth term = a1 + d(n-1)
= 6 + -6(n-1)
= 6 - 6n + 6
= 12-6n

Answer 2

12 - 6n

Explanation:

As this sequence decreases, rather than increases, this tell us that the nth term of this sequence will be minus. The difference from 6 and 0 is 6, telling us that the decrease is by 6 each time. So now we know the nth term of this sequence; -6n, but the sequence of -6n is -6,-12,-18 and so on. We need 6,0,-6. To find out the second part of the nth term find the difference from the sequence given and the sequence of -6n. The difference is 12 because the 6--6 = 12. So now we get the nth term of the sequence -6n + 12 which is written as 12-6n.