NECO 2023 · Paper 1 · Q9

If $a_{n+2} = 0.2a_{n+1} - 0.1a_n$ and $a_1 = 0$ , $a_2 = 1$ , determine the fifth term of the sequence.

Worked solution (try it first)

Put $n = 1$ : $a_3 = 0.2a_2 - 0.1a_1 = 0.2(1) - 0.1(0)$ , which is 0.2.
Put $n = 2$ : $a_4 = 0.2a_3 - 0.1a_2 = 0.04 - 0.1$ , which is $-0.06$ .
Put $n = 3$ : $a_5 = 0.2a_4 - 0.1a_3 = -0.012 - 0.02$ , which is $-0.032$ , option A.