Question

Find the common difference for a_n=1/7+2nGiven: the first term is 1/9

Answer 1

Given:

The sequence is:

`a_n=(1)/(7+2n)`

The first term

`a_1=(1)/(9)`

Required:

Find the common difference of the sequence.

Step-by-step explanation:

The given sequence is

`\begin{gathered} a_(n)=(1)/(7+2n) \\ a_1=(1)/(9) \end{gathered}`

Substitute n = 2

`\begin{gathered} a_2=(1)/(7+2(2)) \\ a_2=(1)/(7+4) \\ a_2=(1)/(11) \end{gathered}`

Substitute n = 3

`\begin{gathered} a_3=(1)/(7+2(3)) \\ a_3=(1)/(7+6) \\ a_3=(1)/(13) \end{gathered}`

Thue the numbers of the sequence are:

`(1)/(9),(1)/(11),(1)/(13),....`

The given sequence is in HP.

Write it in AP as:

`9,11,13`