Question

Write an explicit formula for the sequence 8, 6, 4, 2, 0, ... Then find a14.

Answer 1

$\bf 8~~,~~\stackrel{8-2}{6}~~,~~\stackrel{6-2}{4}~~,~~\stackrel{4-2}{2}~~,~~\stackrel{2-2}{0}$

so, as you can see, the common difference is then -2, and the first term is clearly 8, thus

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\qquad\begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\d=\textit{common difference}\\[-0.5em]\hrulefill\\a_1=8\\d=-2\\n=14\end{cases}\\\\\\a_{14}=8+(14-1)(-2)\implies a_{14}=8-26\implies a_{14}=-18$

Answer 2

Answer:

Explicit formula = $a_n=8+(n-1)\times(-2)$ and $a_14=-18$

Step-by-step explanation:

Formula for nth term in A.P. = $a_n=a+(n-1)d$

a = first term

d= common difference

Given sequence =  8, 6, 4, 2, 0, ...

a = 8

d = 6-8=4-6= -2

So , Explicit formula = $a_n=8+(n-1)\times(-2)$

To find $a_14$

put n =14

$a_14=8+(14-1)\times(-2)$

$a_14=8+13\times(-2)$

$a_14=8-26$

$a_14=-18$

Hence Explicit formula = $a_n=8+(n-1)\times(-2)$ and $a_14=-18$