Find the 18h term of the arithmetic sequence whose common difference is d=4 and whose first term is a, =3.

the 18th term is 71

Step-by-step explanation:

The general form for any term "n" in an arithmetic sequence is:

a(n) = a1 + (n-1) * d

where "d" is the common difference.

So, in our case we have:

a(n) = 3 + (n-1) *4

Therefore, the 18th term will be:

a(18) = 3 + (18 - 1) 4 = 3 + 17 * 4 = 71

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: