Asequence is defined by the recursive function f(n + 1) = f(n) – 2. if f(1) = 10, what is f(3)?

6

Step-by-step explanation:

Lets see what f(2) is.

f(n + 1) = f(n) – 2

We are going to replace n with 1 to get f(2):

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

f(2)=f(1)-2

Since f(1)=10 we can rewrite as:

f(2)=10-2

f(2)=8

We want to find f(3) so now we will replace n with 2:

f(n + 1) = f(n) – 2

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

f(3)=f(2)-2

f(3)=8-2

f(3)=6.

So f(3) is 6.

Another way:

f(n + 1) = f(n) – 2 says you can find the next term by taking previous and minus 2 from it.

So if we start with first term, f(1) , is 10.

Then second term, f(2) , is 10-2=8.

The third term, f(3) , is 8-2=6.

47 - 90 = 43

43 - 180 = x

x = 137

system of linear equation

step-by-step explanation:

as given in the data

a= 20 , b= -12

let us suppose that it is a straight line equation

now we know the formula for the system of linear equation

b= ma + c )

here m is slope of a straight line which is equal to formula

m=   (ii)

and here c is a constant

now putting the value of a and b in equation (ii)

m=

m=

putting the value of a,b and m in equation (i) gives us

-12 = + c

-12=-12 + c

adding 12 to both sides

-12 +12 = -12 +12 +c

0 =c

or c=0

as the value of the constant is zero which gives us that it is a linear equation and this order pair satisfies the system of linear equations.