Find an explicit formula for the arithmetic sequence 170, 85, 0, - 85, ...

D (n) =

Numbers that are presented in sequences are called progressions. There can be three types of this: arithmetic progression, geometric progression and harmonic progression. Let's focus on the arithmetic progression.

Arithmetic progression are numbers in the sequence that has a common difference, denoted as d. One way to find this is to subtract adjacent numbers within the sequence.

85 - 170 = - 85

0 - 85 = - 85

-85 - 0 = - 85

So, there is a pattern that the common difference is - 85. Now, derived formulas are already set conveniently for substitution. For arithmetic progression, the formula is

An = A1 + d (n-1)

where

An is the nth term of the sequence

A1 is the 1st term of the sequence

n is the total number of terms in the sequence

Hence, for this particular sequence, A1 = 170. Substituting,

An = 170 + (-85) (n - 1)

An = 170 - 85 (n-1)

Simplifying further,

An = 170 - 85n + 85

An = 255 - 85n