Question

Write down the first five terms of the sequence a_n=7n/n+2 a1 = a2 = a3 = a4 = a5 =

Answer 1

Explanation

We are required to obtain the first five terms of the sequence below:

`a_n=(7n)/(n+2)`

This can be achieved by substituting for n, the values 1, 2, 3, 4, and 5. This is shown below:

`\begin{gathered} a_(n)=(7n)/(n+2) \\ when\text{ }n=1;\text{ }a_1=(7(1))/(1+2)=(7)/(3) \\ when\text{ n}=2;\text{ a}_2=(7(2))/(2+2)=(7)/(2) \\ when\text{ n}=3;\text{ a}_3=(7(3))/(3+2)=(21)/(5) \\ when\text{ n}=4;\text{ a}_4=(7(4))/(4+2)=(14)/(3) \\ when\text{ n}=5;\text{ }a_5=(7(5))/(5+2)=5 \\ Therefore,\text{ }the\text{ first five terms are }(7)/(3),(7)/(2),(21)/(5),(14)/(3),and\text{ }5. \end{gathered}`

Hence, the answers are:

a₁ = 7/3

a₂ = 7/2

a₃ = 21/5

a₄ = 14/3

a₅ = 5