MATH SOLVE

4 months ago

Q:
# What are the first five terms of the sequence defined by the given function?(1) = -6f(n) = }(n β 1) + 2, for n = 2, 3, 4, ...O A. 6,-4,-2,0, 2B. 2, 8, 14, 20, 26c. 6,-8.-10.-12, -14D. 2.-4.-10.-16, -22

Accepted Solution

A:

Answer:-6,-4,-2,0,2is the answer if I interpreted your recursive sequence equation correctly. Step-by-step explanation:I'm going to assume the following:f(1)=-6f(n)=f(n-1)+2They alread give you the first term is -6.So we want to find the next 4 terms.The second term is given by f(2).So we replace n with 2:f(n)=f(n-1)+2 with n=2f(2)=f(2-1)+2f(2)=f(1)+2f(2)=-6+2f(2)=-4The third term is given by f(3).So we replace n with 3:f(n)=f(n-1)+2 with n=3f(3)=f(3-1)+2f(3)=f(2)+2f(3)=-4+2f(3)=-2The fourth term is given by f(4).We are going to replace n with 4.f(n)=f(n-1)+2 with n=4f(4)=f(4-1)+2f(4)=f(3)+2f(4)=-2+2f(4)=0The fifth term is given by f(5).We will replace n with 5.f(n)=f(n-1)+2 with n=5f(5)=f(5-1)+2f(5)=f(4)+2f(5)=0+2f(5)=2So the first 5 terms are given by the values of:f(1),f(2),f(3),f(4),f(5).The values we got in order are:-6,-4,-2,0,2This should also make sense from reading:f(1)=-6f(n)=f(n-1)+2That bottom equation says to find a term you just add 2 to the previous term. They gave us the first term was -6 and told us just to add 2 to generate the terms after.First term is -6.Second term is -6+2=-4.Third term is -4+2=-2.Fourth term is -2+2=0Fifth tern is 0+2=2.In the future this sequence is called an arithmetic sequence because the term and previous term has the same difference; this is called a commom difference.