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Chapter 12: Q. 34 (page 839)

A brick staircase has a total of 25 steps. The bottom step requires 80 bricks. Each

successive step requires three fewer bricks than the prior step.

(a) How many bricks are required for the top step?

(b) How many bricks are required to build the staircase?

Short Answer

Expert verified

(a) Number of bricks required for the top step are 8.

(b) Total number of bricks required to build the staircase are 1100.

Step by step solution

01

Given information:

Total number of steps, n=25,

Number of bricks for bottom step, a1=80,

Since each successive step requires three less bricks, d=-3

鈭�Sequence will be 80,77,74,.... It is an Arithmetic Sequence.

02

Formulas: 

(1)an=a1+(n-1)d(2)Sn=n2an+a1

03

(a) To find the number of bricks required for the top step ie, an:

Substitute the given values in the first formula, we get,

an=80+(25-1)脳-3

=80+24脳-3

=80-72

=8

04

(b) To find the number of bricks to build the staircase ie, Sn.

Substitute the given values in the second formula, we get,

Sn=25280+8

=252脳88=25脳44

=1100

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Most popular questions from this chapter

Environmental Control: The Environmental Protection Agency (EPA) determines that Maple Lake has 250 tons of pollutants as a result of industrial waste and that 10% of the pollutant present is neutralized by solar oxidation every year. The EPA imposes new pollution control laws that result in 15 tons of new pollutant entering the lake each year. The amount of pollutant in the lake at the end of each year is given by the recursively defined sequence

p0=250;pn=0.9pn-1+15

(a) Determine the amount of pollutant in the lake at the

end of the second year. That is, determine p2 .

(b) Using a graphing utility, provide pollutant amounts for

the next 20 years.

(c) What is the equilibrium level of pollution in Maple

Lake? That is, what is localid="1646823556776" limn鈫�鈭�pn?

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

a1=1;a2=2;an=an-1路an-2

In Problems 17鈥�28, write down the first five terms of each sequence.

tn=(-1)n(n+1(n+2)

In Problems 71-82, find the sum of each sequence.

鈭�(-k=124k)

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

role="math" localid="1646738144824" 12,23,34,45,...
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