What is the sum of a 44 term arithmetic sequence where the first term is -9 and the last term is 120

2442

Step-by-step explanation:

The n th term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d is the common difference

We require to find d knowing that 120 is the 44 th term, thus

= - 9 + 43d = 120 ( add 9 to both sides )

43d = 129 ( divide both sides by 43 )

d = 3

The sum to n terms of an arithmetic sequence is

= [ 2a₁ + (n - 1)d ], hence

= [ (2 × - 9 + (43 × 3) ]

                          = 22(- 18 + 129)

                          = 22 × 111 = 2442

OR

Since the first and last terms in the sequence are known, then

= ( first + last )

= 22(- 9 + 120) = 22 × 111 = 2442

your answer is -9

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.