A sequences is defined by f(0)=-20 f(0)=−20 , f(n)=f(n-1)-5 f(n)=f(n−1)−5 for n≥1 . Complete the expression f(10)=-20- f(10)=−20− ________. Explain your reasoning.

Answer 1

This can be viewed as a linear difference equation: Δf(n) = -5.

The general solution is f(n) = -5n + C where C is an arbitrary constant.

Since f(1) = -20 = -5 + C, C=-15 and the general solution is f(n) = -15 - 5n and

f(10) = -65.

Alternatively you could write out the sequence: -20, -25, -30,....and eventually get to -65.

Or you could get to the arithmetic sequence by observing that f(1) = -20 and the difference is -5, which gets you the same result.