MATH SOLVE

4 months ago

Q:
# Melinda has shown that a function, f(x), increases by 4 for every unit in the domain. What does this prove? The function f(x) is an arithmetic sequence. The function f(x) is a geometric sequence. The function f(x) is not a sequence. This does not prove anything.

Accepted Solution

A:

Answer:-The function f(x) is an arithmetic sequence.

Explanation:-Let [tex]a_1[/tex] be the initial value According to the question[tex]a_2=a_1+4[/tex] [tex]a_3=a_2+4\\\Rightarrow\ a_3=(a_1+4)+4\\\Rightarrow\ a_3=a_1+4+4\\\Rightarrow\ a_3=a_1+2(4)\\\Rightarrow\ a_3=a_1+2\times4\\\Rightarrow\ a_3=a_1+(3-1)4[/tex] and so on Thus, we can write a formula for the term n of an arithmetic sequence in the form:[tex]a_n=a_1+(n-1)4[/tex] where, n=1,2,3,4,....4= common differenceTherefore, the function f(x) is an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term increases or decreases by a constant number.

Explanation:-Let [tex]a_1[/tex] be the initial value According to the question[tex]a_2=a_1+4[/tex] [tex]a_3=a_2+4\\\Rightarrow\ a_3=(a_1+4)+4\\\Rightarrow\ a_3=a_1+4+4\\\Rightarrow\ a_3=a_1+2(4)\\\Rightarrow\ a_3=a_1+2\times4\\\Rightarrow\ a_3=a_1+(3-1)4[/tex] and so on Thus, we can write a formula for the term n of an arithmetic sequence in the form:[tex]a_n=a_1+(n-1)4[/tex] where, n=1,2,3,4,....4= common differenceTherefore, the function f(x) is an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term increases or decreases by a constant number.