An arithmetic sequence is defined by f(n) = 52 + (n − )
for 1 what are the domain and range values of f(n)?

D = {n|n∈N}

R = {f|f∈Z|f≤52}

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.)