Asequence is defined by the function f(n)=f(n-1)+5. where n represents the number of the term for n> 1 and f(1)=-4. what are the first four terms of the sequence

The first four terms of the above sequence are 1, 6, 11, 16.

Step-by-step explanation:

A sequence is defined by the function f(n)=f(n-1)+5.

Where n represents the number of the term for n>1

First Put n = 2

f(2)=f(2-1)+5.

    = f (1) + 5

    = -4 + 5

    = 1

Second Put n = 3

f(3)=f(3-1)+5.

    = f (2) + 5

    = 1 + 5

    = 6

Third Put n = 4

f(4)=f(4-1)+5.

    = f (3) + 5

    =  6+ 5

    = 11

Second Put n = 5

f(5)=f(5-1)+5.

    = f (4) + 5

    = 11 + 5

    = 16

Therefore the first four terms of the above sequence are 1, 6, 11, 16.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3