Question

Find the first four terms of the sequence given by the following.1) 2n2) 4n+ 1n=1, 2, 3, ...

Answer 1

Given:

1) The sequence is given as,

`\begin{gathered} 1)\text{ 2n } \\ 2)\text{ 4n + 1} \end{gathered}`

Required:

First four terms of the given sequence.

Step-by-step explanation:

1) The sequence is given as,

`2n`

For n = 1,

`\begin{gathered} 2n\text{ = 2\lparen1\rparen} \\ 2n\text{ = 2} \end{gathered}`

For n = 2,

`\begin{gathered} 2n\text{ = 2\lparen2\rparen} \\ 2n\text{ = 4} \end{gathered}`

For n = 3,

`\begin{gathered} 2n\text{ = 2\lparen3\rparen} \\ 2n\text{ = 6} \end{gathered}`

For n = 4,

`\begin{gathered} 2n\text{ = 2\lparen4\rparen} \\ 2n\text{ = 8} \end{gathered}`

Answer:

Thus the first 4 terms of the given sequence are 2, 4, 6, and 8.

2) The sequence is given as,

`4n\text{ + 1}`

For n = 1,

`\begin{gathered} 4n\text{ + 1 = 4\lparen1\rparen + 1} \\ 4n\text{ + 1 = 4 + 1} \\ 4n\text{ + 1 = 5} \end{gathered}`

For n = 2,

`\begin{gathered} 4n\text{ + 1 = 4\lparen2\rparen + 1} \\ 4n\text{ + 1 = 8 + 1} \\ 4n\text{ + 1 = 9} \end{gathered}`

For n = 3,

`\begin{gathered} 4n\text{ + 1 = 4\lparen3\rparen + 1} \\ 4n\text{ + 1 = 12 + 1} \\ 4n\text{ + 1 = 13} \end{gathered}`

For n = 4

`\begin{gathered} 4n+1\text{ = 4\lparen4\rparen + 1} \\ 4n+1\text{ = 16 + 1} \\ 4n+1\text{ = 17} \end{gathered}`

Answer:

Thus the first four terms of the given sequence are 5, 9, 13, and 17