## Arithmetic Series Worksheet Solution5

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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