Question

Find the respective patterns for these sequences:
a = 1, 2, 3, 4...
b = 0, 2, 4, 6, 8...

Answer 1

On oberservation,
(i) $a=1,2,3,\mathrm{4...}$
Here, we have a pattern of $(n+1)$ where n is a whole number.
By substituting $n=0,1,2,\mathrm{3..}$,
$a=0+1,1+1,2+1,3+\mathrm{1...}$
$=1,2,3,\mathrm{4...}\Rightarrow n+1$


(ii) $b=0,2,4,6,\mathrm{8...}$
Here, we have pattern of $2n$ where $n$ is a whole number.
By substituting $n=0,1,2,\mathrm{3..}$,
$b=2\times 0,2\times 1,2\times 2,2\times \mathrm{3...}$
$=0,2,4,\mathrm{6...}\Rightarrow 2n$