Question

An arithmetic sequence is defined by the recursive formula t1 = 44, tn + 1 = tn + 16, where n ∈N and n ≥ 1. Which is the general term of the sequence? A) tn = 44 + (n - 1)16, where n ∈N and n ≥ 1 B) tn = 44 + (n + 1)16, where n ∈N and n ≥ 1 C) tn = 44 + (n - 2)16, where n ∈N and n ≥ 1 D) tn + 1 = 44 + (n - 1)16, where n ∈N and n ≥ 0

Answer 1

$\begin{cases}t_1=44\\t_{n+1}=t_n+16&\text{for }n>1\end{cases}$

According to this rule, we get

$t_2=t_1+16$

$t_3=t_2+16=t_1+2\cdot16$

$t_4=t_3+16=t_1+3\cdot16$

and so on, up to

$t_n=t_{n-1}+16=t_{n-2}+2\cdot16=\cdots$

$\implies t_n=t_1+(n-1)\cdot16$

Then

$t_n=44+16(n-1)=16n+28$

which matches answer A.