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.)

the answer is 40.

proof: