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Sagot :
Given:
1) The sequence is given as,
[tex]\begin{gathered} 1)\text{ 2n } \\ 2)\text{ 4n + 1} \end{gathered}[/tex]Required:
First four terms of the given sequence.
Explanation:
1) The sequence is given as,
[tex]2n[/tex]For n = 1,
[tex]\begin{gathered} 2n\text{ = 2\lparen1\rparen} \\ 2n\text{ = 2} \end{gathered}[/tex]For n = 2,
[tex]\begin{gathered} 2n\text{ = 2\lparen2\rparen} \\ 2n\text{ = 4} \end{gathered}[/tex]For n = 3,
[tex]\begin{gathered} 2n\text{ = 2\lparen3\rparen} \\ 2n\text{ = 6} \end{gathered}[/tex]For n = 4,
[tex]\begin{gathered} 2n\text{ = 2\lparen4\rparen} \\ 2n\text{ = 8} \end{gathered}[/tex]Answer:
Thus the first 4 terms of the given sequence are 2, 4, 6, and 8.
2) The sequence is given as,
[tex]4n\text{ + 1}[/tex]For n = 1,
[tex]\begin{gathered} 4n\text{ + 1 = 4\lparen1\rparen + 1} \\ 4n\text{ + 1 = 4 + 1} \\ 4n\text{ + 1 = 5} \end{gathered}[/tex]For n = 2,
[tex]\begin{gathered} 4n\text{ + 1 = 4\lparen2\rparen + 1} \\ 4n\text{ + 1 = 8 + 1} \\ 4n\text{ + 1 = 9} \end{gathered}[/tex]For n = 3,
[tex]\begin{gathered} 4n\text{ + 1 = 4\lparen3\rparen + 1} \\ 4n\text{ + 1 = 12 + 1} \\ 4n\text{ + 1 = 13} \end{gathered}[/tex]For n = 4
[tex]\begin{gathered} 4n+1\text{ = 4\lparen4\rparen + 1} \\ 4n+1\text{ = 16 + 1} \\ 4n+1\text{ = 17} \end{gathered}[/tex]Answer:
Thus the first four terms of the given sequence are 5, 9, 13, and 17
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