Question

Match the APs to their $n^{\text{th}}$ terms.

• A. $3n+2$
• B. $2n-1$
• C. $3n-2$
• D. $6-n$

Answer 1

The $n^{\text{th}}$ term of an AP with first term $a$ and common difference $d$ is given by
$a_n=a+(n-1)d.$

In the AP 5, 8, 11, 14, ... $a=5,d=8-5=3.$
$\therefore a_n=5+(n-1)3=3n+2$

In the AP 1, 3, 5, 7, ... $a=1,d=3-1=2$
$\therefore a_n=1+(n-1)2=2n-1$

In the AP 1, 4, 7, 10, ...$a=1,d=4-1=3$
$\therefore a_n=1+(n-1)3=3n-2$

In the AP 5, 4, 3, 2, ...$a=5,d=4-5=-1$
$\therefore a_n=5+(n-1)(-1)=6-n$