The first term of an arithmetic sequence is -27. the common difference of the sequence is 6. What is the sum of the first 30 terms

1800

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

= [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 27 and d = 6, thus

= [ (2 × - 27) + (29 × 6) ]

     = 15( - 54 + 174)

     = 15(120)

     = 1800

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:

the answer is the third / last answer

step-by-step explanation: