Question

Write an explicit equation for the following sequence.

100, 97, 94, 91, ...

Answer 1

`a_(n)` = 103 - 3n

Explanation:

there is a common difference between consecutive terms , that is

97 - 100 = 94 - 97 = 91 - 94 = - 3

This indicates the sequence is arithmetic with explicit equation

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 100 and d = - 3 , then

`a_(n)` = 100 - 3(n - 1) = 100 - 3n + 3 = 103 - 3n