Question

Find a pattern for these sequences:
a = 1, 2, 3, 4...
b = 0, 2, 4, 6, 8...
c = 1, 3, 5, 7...

• A. a = 2n; b=n + 1; c=2n + 1
• B. a = n + 1 ;b = 2n;c = 2n + 1
• C. a = 2n + 1;b = n + 1;c = 2n
• D. a = 2n; b = 2n + 1;c = n + 1

Answer 1

The correct option is B

a = n + 1 ;b = 2n;c = 2n + 1

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


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

(iii) $c=1,3,5,\mathrm{7...}$
Here, we have pattern of $(2n+1)$ where $n$ is a whole number.
By substituting $n=0,1,2,\mathrm{3..}$,
$b=(2\times 0)+1,(2\times 1)+1,(2\times 2)+1,...$
$=0+1,2+1,4+1,5+\mathrm{1...}$
$=1,3,5,\mathrm{7...}\Rightarrow 2n+1$

$\therefore$$a=n+1;b=2n;c=2n+1$