Question 9
Exercise 5. Consider the following pattern:
$$\begin{aligned}1&=1^2\\1+3&=2^2\\1+3+5&=3^2\\1+3+5+7&=4^2\\&\ldots\\1+3+5+\ldots+(2k-1)&=144\\&\ldots\end{aligned}$$
a) Write down the 8th line in the pattern.
b) Find the value of $k$.
**Editorial input convention:** Line n sums the first n positive odd integers. Enter the complete eighth-line equality, then k, separated by a semicolon; use ^ for exponents. A format example, not the answer: 1+3=2^2=4; 2.
**Editorial input note:** Use no spaces anywhere in your entry. Apply this rule to the format example above.
$$\begin{aligned}1&=1^2\\1+3&=2^2\\1+3+5&=3^2\\1+3+5+7&=4^2\\&\ldots\\1+3+5+\ldots+(2k-1)&=144\\&\ldots\end{aligned}$$
a) Write down the 8th line in the pattern.
b) Find the value of $k$.
**Editorial input convention:** Line n sums the first n positive odd integers. Enter the complete eighth-line equality, then k, separated by a semicolon; use ^ for exponents. A format example, not the answer: 1+3=2^2=4; 2.
**Editorial input note:** Use no spaces anywhere in your entry. Apply this rule to the format example above.