Question

Find an explicit formula for the arithmetic sequence: 81, 54, 27, 0

Answer 1

$\bf 81~~,~~\stackrel{81-27}{54}~~,~~\stackrel{54-27}{27}~~,~~\stackrel{27-27}{0}~~,~...\qquad \qquad \stackrel{\textit{common difference}}{d = -27} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=81\\ d=-27 \end{cases} \\\\\\ a_n=81+(n-1)(-27)\implies a_n=81-27n+27\implies a_n=108-27n$

Answer 2

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here d = 54 - 81 = 27 - 54 = - 27 and a₁ = 81, hence

$a_{n}$ = 81 - 27(n - 1) = 81 - 27n + 27 = 108 - 27n