Question

Which of the following is a function rule for the sequence 3, 8, 13, 18, 23, ...? A(n) = 5 + (n - 1)(3)A(n)= 3 + (n - 1)(5) A(n) = 1 + (n = 115) A(n) = 1 + (n - 1)(3)

Answer 1

Given:

`\begin{gathered} \text{The sequence;} \\ 3,8,13,18,23,\ldots \end{gathered}`

The sequence given is an arithmetic progression because it increases by a common difference.

Hence, the function rule for the sequence will follow that of an arithmetic progression (A.P).

The nth term of an A.P is given by;

`\begin{gathered} a_n=a+(n-1)d_{} \\ \text{where;} \\ a_n\text{ is the nth term} \\ a\text{ is the first term} \\ n\text{ is the number of terms} \\ d\text{ is the co}mmon\text{ difference} \end{gathered}`

For the sequence given;

`\begin{gathered} 3,8,13,18,23,\ldots \\ \\ a=3 \\ d=8-3\text{ or 13-8 or 18-13 or 23-18} \\ d=5 \\ \\ \text{Hence, substituting these values into the nth term of an A.P to get the rule,} \\ a_n=a+(n-1)d_{} \\ A(n)=3+(n-1)(5) \end{gathered}`

Therefore, the function rule for the sequence is;

`A(n)=3+(n-1)(5)`