An arithmetic sequence is defined by f (n) = 52 + (n - 1) (-7)

for 1 What are the domain and range values of f (n) ?

D = n∈N

R = f

Step-by-step explanation:

Since n represents the terms number, it cannot be less than 1. It does not make sense to have the 0th term. n is restricted to all natural numbers, represented N. Natural numbers are positive whole numbers starting from 1 (1, 2, 3, ...).

For the range, they are the term values. Since the lowest value of n is 1, solve for f (1).

f (1) = 52 + (1 - 1) (-7)

f (1) = 52 < = one of the restrictions.

There is no highest possible value of n, therefore there is no corresponding restriction for f. To decide if f is ≤ or ≥ than 52, determine if the next terms in the sequence gets smaller or larger.

f (2) = 52 + (2 - 1) (-7)

f (2) = 45

The sequence is getting smaller. This means that f≤52. Because f can keep getting smaller and smaller, it can go into negative values. It will never be a fractional number, so we say f can be an integer, represented by Z. Integers are numbers that have no partials and include positive and negative. (We don't use the letter "I" because it's hard to see.)