Respuesta :
We have that an arithmetic sequence can be defined by the following explicit formula:
[tex]a_n=a_1+(n-1)\cdot d[/tex]where n represents the index of each term in the sequence and d represents the common difference beteen each term. a1 is the first term of the sequence.
In this case we have that the first term is a1 = 6, and also we have that a3=14. We can use the formula to find the common difference:
[tex]\begin{gathered} a_3=a_1+(3-1)d \\ \Rightarrow a_3=a_1+2d \\ \Rightarrow14=6+2d \end{gathered}[/tex]solving for d, we get:
[tex]\begin{gathered} 2d+6=14 \\ \Rightarrow2d=14-6=8 \\ \Rightarrow d=\frac{8}{2}=4 \\ d=4 \end{gathered}[/tex]therefore, the value of d is d = 4.
We have now the explicit formula for the sequence:
[tex]\begin{gathered} a_n=6_{}+4(n-1) \\ \end{gathered}[/tex]then, for the 20th term, we have to make n = 20 on the formula, and we get the following:/
[tex]\begin{gathered} a_{20}=6+4(20-1)=6+4(19)=6+76=82 \\ \Rightarrow a_{20}=82 \end{gathered}[/tex]therefore, the 20th term is 82
