A roll of paper towels is wound around a hollow cardboard tube. the
cardboard tube in the middle of the roll has an outside radius of 2.4 cm. the
thickness of the paper is 0.3 mm. the sequence of distances of the loops of
paper away from the center of the roll (in centimeters) is the following:
21, 22, az, a4 a5, ... = 2.40, 2.43, 2.46, 2.49, 2.52, ..
what is the radius of the 85th loop of paper, starting from the center of the
tube?
a. 4.95 cm
b. 4.86 cm
c. 4.92 cm
d. 4.89 cm

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varshamittal029 varshamittal029 · Answer 1 · 2022-06-29T06:13:26+02:00

The correct Option is Option C: The radius of the cardboard tube of 85th loop of paper is 4.92cm

The arithmetic sequence is the sequence where every term is increased or decreased by a fixed number from the previous number.

Here the outer radius of the tube is 2.4 cm

the thickness of the paper is 0.3mm= 0.03cm

i.e. in every loop the increase in the radius of the loop is 0.03cm

then the radius in every sequence will be 2.40, 2.43, 2.46, 2.49, 2.52, .....

so here it is clear that it is an arithmetic sequence with a common difference of 0.03.

nth term of the sequence, aₙ = a₁ + (n - 1)d where a₁ is the first term, n is the index of the loop, and d is a common difference.

here a₁ =2.40

d=0.03

n=85

the radius of tube of the 85th loop will be= r= 2.40+(85-1)0.03= 2.40+ 2.52= 4.92

Therefore The radius of the cardboard tube of the 85th loop of paper is 4.92cm

Learn more about the arithmetic sequence

here: https://brainly.com/question/6561461

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