4) An arithmetic sequence has a 7th term of 54 and a 13th term of 94. Find the common difference (Write as a fraction)
Plz help

a = 14 and d = 6.67

Step-by-step explanation:

The nth term of an AP is given by :

Where

a is the first term and d is the common difference

ATQ,

An arithmetic sequence has the 7th term of 54 and the 13th term of 94 i.e.

Subtract equation (2) from (1).

a+6d-(a+12d) = 54-94

a+6d-a-12d = -40

-6d = -40

d = 6.67

Put the value of d in equation (1).

or

a = 14

Hence, the first term is 14 and the common difference is 6.67.

11 feet 6 inches and 8 feet 6 inches

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: