Question

Write the first six terms of each arithmetic sequence:a,=200d=20

Answer 1

Recall that the nth term of an arithmetic sequence is as follows:

`\begin{gathered} a_n=a_1+d(n-1), \\ where\text{ }a_1\text{ is the first element and d is the common difference between terms.} \end{gathered}`

We know that:

`\begin{gathered} a_1=200, \\ d=20. \end{gathered}`

Therefore:

1) The second term of the given arithmetic sequence is:

`a_2=200+20(2-1),`

simplifying the above result we get:

`a_2=200+20(1)=220.`

2) The third term of the given arithmetic sequence is:

`a_3=200+20(3-1)=200+20(2)=240.`

3) The fourth therm is:

`a_4=200+20(4-1)=200+20(3)=260.`

4) The fifth term is:

`a_5=200+20(5-1)=200+20(4)=280.`

5) The sixth term is:

`a_6=200+20(6-1)=200+20(5)=300.`

Answer: The first six terms of the given sequence are:

`200,\text{ }220,\text{ }240,\text{ }260,\text{ }280,\text{ }300.`