Arithmetic Series Worksheet Solution5





In the page arithmetic series worksheet solution5 you are going to see solution of each questions from the arithmetic series worksheet.

(13) A construction company will be penalized each day of delay in construction for bridge. The penalty will be $4000 for the first day and will increase by $1000 for each following day. Based on its budget, the company can afford to pay a maximum of $ 165000 toward penalty. Find the maximum number of days by which the completion of work can be delayed

Solution:

Let us write the penalty amount paid by the construction company from the first day as sequence

       4000,5000,6000,..............

The company can pay 165000 as penalty for this delay at maximum.

So we have to write this amount as series 4000 + 5000 + 6000 + ..... and the sum of the penalty amount is 165000.

Sn= 165000

a = 4000 d = 1000

(n/2)[2a+(n-1)d] = 165000

(n/2)[ 2 (4000) + (n-1) 1000 ] = 165000

(n/2)[ 8000 + (n-1) 1000 ] = 165000

(n/2)[ 8000 + 1000 n- 1000 ] = 165000

(n/2)[ 7000 + 1000 n ] = 165000

n[ 7000 + 1000 n ] = 165000 x 2

7000 n + 1000 n² = 330000

divided by 10000 => 7n + n² - 330

n² + 7 n - 330 = 0

(n-15)(n+22)= 0

n = 15,-22

Here n represents number of days delayed. So it must be positive.Therefore the correct answer is 15.


(14) The sum of $1000 is deposited every year at 8% simple interest. Calculate the interest at the end of each year. Do these interest amounts form an A.P?. If so,find the total interest at the end of 30 years.

Solution:

First let us find the interest amount from simple interest formula.

  S.I = (PNR)/100

       = (1000 x 1 x 8)/100

       = 80

1000,1080,1160,.........

the interest amounts from the first year are 80,160,240..........

This sequence is A.P. From this we have to find the sum of 30 terms . Because we need to find the interest amount for 30 years.

a = 80 d = 160 - 80    n = 30

            = 80

Sn = (n/2) [2a + (n-1) d]

     = (30/2) [2(80) + (30-1) 80]

     = 15 [160 + 29(80)]

     = 15 [160 + 2320]

     = 15 [2480]

     = 37200         



These are the contents in the page arithmetic series worksheet solution5.  
arithmetic series worksheet solution5