Question 5
Consider the following pattern:
$1=1^2$
$1+3=2^2$
$1+3+5=3^2$
$1+3+5+7=4^2$
$\ldots$
$1+3+5+\cdots+(2k-1)=144$
$\ldots$
a) Write down the 8th line in the pattern.
b) Find the value of k.
**Editorial note for this self-study exercise:** Write the full equation for part (a), then give k for part (b). This response is marked manually so equivalent mathematical notation can be credited.
$1=1^2$
$1+3=2^2$
$1+3+5=3^2$
$1+3+5+7=4^2$
$\ldots$
$1+3+5+\cdots+(2k-1)=144$
$\ldots$
a) Write down the 8th line in the pattern.
b) Find the value of k.
**Editorial note for this self-study exercise:** Write the full equation for part (a), then give k for part (b). This response is marked manually so equivalent mathematical notation can be credited.