Question

***WILL MEDAL***
A sequence is defined by the formula f(n + 1) = f(n) – 3. If f(4) = 22, what is f(1)?

Answer 1

Let n = 3

f(3+1) = f(3) - 3

f(4) = f(3) - 3

f(3) = f(4) + 3 = 22 + 3 = 25

Let n =2

f(3) = f(2) - 3

f(2) = f(3) + 2 = 25 + 3 = 28

Let n = 1

f(2) = f(1) - 3

f(1) = f(2) + 3 = 28 + 3 = 31

Answer 2

Another solution:

f(n+1)- f(n) = -3 = d

d = -3 (common difference)

and we have a sequence which a_{4} = 22 (4th term)

a_{4} = a_{0} + d(n-1)

22 = a_{0} -3(4-1)

a{0} = 22 + 9 = 31