Explain the The fifth term of a non-linear sequence is 324. The term-to-term rule is ‘multiply by 3?
Work out the second term of the sequence.
Explain the method you used to solve this problem.

a2=12 (the second term of the sequence is 12)

Step-by-step explanation:

a5=324

If the term to term rule is multiply by any number, we deal with geometrical sequence

The formula you should use is an= a1*r^(n-1)  where n is the number of the term which we know. In our case we know

a5, so use 5 instead of n

Then you have a5=a1*r^4 where r is the number 3 (because each next term is greater than previous in 3 times)

a5=324

324= a1*3^4

324=a1*81

a1=4 (We find the first term of sequence, because having it you can easily search for every term )

Return to the formula an= a1*r^n-1

Now search for the second term using 2 instead of n in the formula

a2= a1*r^1

a2=a1*r, a1=4, r=3

a2=4*3=12

(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

f is the midpoint of