Question

The following table contains the first 5 terms of an infinite arithmetic sequence. What is the 7th term?

Answer 1

f(n) is an arithmetic sequence, so the difference between any two consecutive terms is the same. For instance,

f(2) - f(1) = -0.6 - 0.7 = -1.3

so for all natural numbers n, we should have

f(n) - f(n - 1) = -1.3

Then

f(6) - f(5) = -1.3 ⇒ f(6) = -4.5 - 1.3 = -5.8

f(7) - f(6) = -1.3 ⇒ f(7) = -5.8 - 1.3 = -7.1