Explanation
We are required to obtain the first five terms of the sequence below:
[tex]a_n=\frac{7n}{n+2}[/tex]
This can be achieved by substituting for n, the values 1, 2, 3, 4, and 5. This is shown below:
[tex]\begin{gathered} a_{n}=\frac{7n}{n+2} \\ when\text{ }n=1;\text{ }a_1=\frac{7(1)}{1+2}=\frac{7}{3} \\ when\text{ n}=2;\text{ a}_2=\frac{7(2)}{2+2}=\frac{7}{2} \\ when\text{ n}=3;\text{ a}_3=\frac{7(3)}{3+2}=\frac{21}{5} \\ when\text{ n}=4;\text{ a}_4=\frac{7(4)}{4+2}=\frac{14}{3} \\ when\text{ n}=5;\text{ }a_5=\frac{7(5)}{5+2}=5 \\ Therefore,\text{ }the\text{ first five terms are }\frac{7}{3},\frac{7}{2},\frac{21}{5},\frac{14}{3},and\text{ }5. \end{gathered}[/tex]
Hence, the answers are:
a₁ = 7/3
a₂ = 7/2
a₃ = 21/5
a₄ = 14/3
a₅ = 5
