Find a formula for the general term of the sequence 4 2 , − 5 4 , 6 8 , − 7 16 , 8 32 , assuming that the pattern of the first few terms continues. SOLUTION We are given that a1 = 4 2 a2 = − 5 4 a3 = 6 8 a4 = − 7 16 a5 = 8 32 . Notice that the numerators of these fractions start with 4 and increase by whenever we go to the next term. The second term has numerator 5, the third term has numerator 6; in general, the nth term will have numerator . The denominators are powers of , so an has denominator . The signs of the terms are alternately positive and negative so we need to multiply by a power of −1. Here we want to start with a positive term and so we use (−1)n − 1 or (−1)n + 1. Therefore, an = (−1)n − 1 · .

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

b. 2 and 4

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.