2019 Nov P1 Q2

Question 2

$2.1$ Given the quadratic sequence: $\:321 \,; 290 \,; 261 \,; 234 \,; ...$
$\quad 2.1.1$	Write down the values of the next TWO terms of the sequence.	$(2)$
$\quad 2.1.2$	Determine the general term of the sequence in the form $\:T_n=an^2+bn+c$ .	$(4)$
$\quad 2.1.3$	Which term(s) of the sequence will have a value of $74$ ?	$(4)$
$\quad 2.1.4$	Which term in the sequence has the least value?	$(2)$
$2.2$ Given the geometric series: $\, \frac{\displaystyle5}{\displaystyle8}+\frac{\displaystyle5}{\displaystyle16}+\frac{\displaystyle5}{\displaystyle32}+...=K$
$\quad 2.2.1$	Determine the value of $K$ if the series has $21$ terms.	$(3)$
$\quad 2.2.2$	Determine the largest value of $n$ for which $\:T_n>\frac{\displaystyle5}{\displaystyle8192}$	$(4)$
		$\textbf{[19]}$