Question

Tn=n^(2)+5 Given the formula for the nth term, state the first 5 terms of each sequence.

Answer 1

The given nth term of the sequence is:

`t_n=n^2+5`

It is required to find the first 5 terms of each sequence.

To do this, substitute n=1,2,3,4,5 into the formula for the nth term of the sequence:

`\begin{gathered} t_n=n^2+5 \\ \text{ For }n=1,\text{ }t_1=1^2+5=1+5=6 \\ \text{For }n=2,\text{ }t_1=2^2+5=4+5=9 \\ \text{For }n=3,\text{ }t_1=3^2+5=9+5=14 \\ \text{For }n=4,\text{ }t_1=4^2+5=16+5=21 \\ \text{For }n=5,\text{ }t_1=5^2+5=25+5=30 \end{gathered}`

The first 5 terms of the sequence are 6, 9, 14, 21, 30.