2020 Nov P1 Q2

Question 2

$2.1$	$7 \,; x \,; y \,; -11 \,; ...$ is an arithmetic sequence. Determine the values of $x$ and $y$ .	$(4)$
$2.2$	Given the quadratic number pattern: $\, -3 \,; 6 \,; 27 \,; 60 \,; ...$
$\quad 2.2.1$	Determine the general term of the pattern in the form $\:T_n=an^2+bn+c$ .	$(4)$
$\quad 2.2.2$	Calculate the value of the $50^{th}$ term of the pattern.	$(2)$
$\quad 2.2.3$	Show that the sum of the first $n$ first-differences of this pattern can be given by $\:S_n=6n^2+3n$ .	$(3)$
$\quad 2.2.4$	How many consecutive first-differences were added to the first term of the quadratic number pattern to obtain a term in the quadratic number pattern that has a value of $21\,060$ ?	$(4)$
		$\textbf{[17]}$