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.