Sequences
We want to find the five terms of the sequence:
f (n) = 2.2 · f (n - 1)
where f (1) = 10
Replacing when n = 2:
f (n) = 2.2 · f (n - 1)
f (2) = 2.2 · f (2 - 1)
f (2) = 2.2 · f (1) [f(2- 1 )= f(1)]
f (2) = 2.2 · 10 [f (1) = 10]
f (2) = 22 [2.2 · 10 = 22]
f(2) = 22
Replacing when n = 3:
f (n) = 2.2 · f (n - 1)
f (3) = 2.2 · f (3 - 1)
f (3) = 2.2 · f (2) [f(3- 1 )= f(2)]
f (3) = 2.2 · 22 [f (2) = 22]
f (3) = 48.4 [2.2 · 22 = 48.4]
f (3) = 48.4
Replacing when n = 4:
f (n) = 2.2 · f (n - 1)
f (4) = 2.2 · f (4 - 1)
f (4) = 2.2 · f (3) [f(4- 1 )= f(3)]
f (4) = 2.2 · 48.4 [f (3) = 48.4]
f (4) = 106.48 [2.2 · 48.4 = 106.48]
f (4) = 106.48
Replacing when n = 5:
f (n) = 2.2 · f (n - 1)
f (5) = 2.2 · f (5 - 1)
f (5) = 2.2 · f (4) [f(5- 1 )= f(4)]
f (5) = 2.2 · 106.48 [f (4) = 106.48]
f (5) = 234.256 [2.2 · 106.48 = 234.256]
f (5) = 234.256
Answer: the five first terms of the sequence are: 10, 22, 48.4, 106.48, 234.256