Respuesta :
[tex]\bf 8~~,~~\stackrel{8-2}{6}~~,~~\stackrel{6-2}{4}~~,~~\stackrel{4-2}{2}~~,~~\stackrel{2-2}{0}[/tex]
so, as you can see, the common difference is then -2, and the first term is clearly 8, thus
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\qquad\begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\d=\textit{common difference}\\[-0.5em]\hrulefill\\a_1=8\\d=-2\\n=14\end{cases}\\\\\\a_{14}=8+(14-1)(-2)\implies a_{14}=8-26\implies a_{14}=-18[/tex]
Answer:
Explicit formula = [tex]a_n=8+(n-1)\times(-2)[/tex] and [tex]a_14=-18[/tex]
Step-by-step explanation:
Formula for nth term in A.P. = [tex]a_n=a+(n-1)d[/tex]
a = first term
d= common difference
Given sequence = 8, 6, 4, 2, 0, ...
a = 8
d = 6-8=4-6= -2
So , Explicit formula = [tex]a_n=8+(n-1)\times(-2)[/tex]
To find [tex]a_14[/tex]
put n =14
[tex]a_14=8+(14-1)\times(-2)[/tex]
[tex]a_14=8+13\times(-2)[/tex]
[tex]a_14=8-26[/tex]
[tex]a_14=-18[/tex]
Hence Explicit formula = [tex]a_n=8+(n-1)\times(-2)[/tex] and [tex]a_14=-18[/tex]
