Question

12
which function represents the sequence in the table? (afgr.9a)

n	$a_n$
2	-1
3	1
4	3
5	5
...	...

a) $a_n = 2a_{n-1} - 5$, $a_1 = -3$
b) $a_n = a_{n-1} + 2$, $a_1 = -3$
c) $a_n = 2a_{n-1} - 3$, $a_1 = -5$
d) $a_n = a_{n-1} + 1$, $a_1 = -5$

Explanation:

Step1: Check initial term

From the table, when $n=1$, $a_1=-3$. This eliminates options C and D, which have $a_1=-5$.

Step2: Test recursive formula for A

Use $a_1=-3$ in option A: $a_2=2a_1-5=2(-3)-5=-6-5=-11$. But the table shows $a_2=-1$, so A is invalid.

Step3: Test recursive formula for B

Use $a_1=-3$ in option B: $a_2=a_1+2=-3+2=-1$, which matches the table.
Verify next term: $a_3=a_2+2=-1+2=1$, which matches.
Verify $a_4=a_3+2=1+2=3$, which matches, and $a_5=a_4+2=3+2=5$, which also matches.

Answer:

B. $a_n = a_{n-1} + 2$, $a_1 = -3$