Consider the following number pattern: State a rule of the number pattern above. Hence complete the

Question

Consider the following number pattern:

Hence complete the following table:

Row Number	Sum of the Numbers of the Row, $S_n$
$1$	$ 1 = 1 = 2^0$
$2$	$ 1 + 1 = 2 = 2^1$
$3$	$ 1 + 2 + 1 = 4 = 2^2$
$4$	$ 1 + 3 + 3 + 1 = 8 = 2^3$
$5$	$ 1 + 4 + 6 + 4 + 1 = 16 = 2^4$
$6$
$7$
...	...
$n$	$1 + (n - 1) + ... + (n - 1) + 1 = $ ________

Accepted Answer

(i) Pascal's triangle rule (ii) $1+5+10+10+5+1=32=2^5$ $1+6+15+20+15+6+1=64=2^6$ $S_n=2^{n-1}$

Row Number	Sum of the Numbers of the Row, \(S_n\)
\(1\)	\( 1 = 1 = 2^0\)
\(2\)	\( 1 + 1 = 2 = 2^1\)
\(3\)	\( 1 + 2 + 1 = 4 = 2^2\)
\(4\)	\( 1 + 3 + 3 + 1 = 8 = 2^3\)
\(5\)	\( 1 + 4 + 6 + 4 + 1 = 16 = 2^4\)
\(6\)
\(7\)
...	...
\(n\)	\(1 + (n - 1) + ... + (n - 1) + 1 = \) ________

Number Patterns