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Sagot :
Solution:
Given the sequence;
[tex]-2,1,4,7,10,...[/tex]The nth term of an arithmetic sequence is;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \\ Where\text{ }a_1=first\text{ }term,d=common\text{ }difference \end{gathered}[/tex]The common difference, d, is the difference between the consecutive terms of an arithmetic sequence.
[tex]\begin{gathered} d=a_2-a_1 \\ \\ Where\text{ }a_2=second\text{ }term \end{gathered}[/tex]Given;
[tex]\begin{gathered} a_2=1,a_1=-2 \\ \\ d=1-(-2) \\ \\ d=3 \end{gathered}[/tex]Thus, the 14th term is;
[tex]\begin{gathered} n=14,d=3,a_1=-2 \\ \\ a_{14}=-2+(14-1)(3) \\ \\ a_{14}=-2+(13)(3) \\ \\ a_{14}=-2+39 \\ \\ a_{14}=37 \end{gathered}[/tex]ANSWER: 37
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