Question

8, 6, 4, 2, 0, ...

The first 5 terms of a linear sequence are shown above.
What is the 100th term in the sequence?

Answer 1

9514 1404 393

Answer:

-190

Explanation:

The n-th term of an arithmetic (linear) sequence is given by ...

an = a1 +d(n -1)

where a1 is the first term (8) and d is the common difference. We note that each term is 2 less than the one before, so the common difference is -2.

an = 8 -2(n -1)

Then the 100th term is ...

a100 = 8 - 2(100 -1) = 8 -198 = -190

The 100th term is -190.