Question

In an arithmetic sequence {an}, if a1 = 5 and d = 3, find a72. A) 216 B) 218 C) 221 D) 223

Answer 1

The arithmetic sequence with the given condition is determined recursively by

$\begin{cases}a_1=5\\a_n=a_{n-1}+3&\text{for }n>1\end{cases}$

So we have

$a_2=a_1+3$

$a_3=a_2+3=a_1+3(2)$

$a_4=a_3+3=a_1+3(3)$

and so on with the general pattern

$a_n=a_1+3(n-1)$

This means the 72nd term in the sequence is

$a_{72}=a_1+3(72-1)=5+3(71)=218$

so the answer is B.