Sum of First n Terms of AP


 
 
Concept Explanation
 

Sum of First n Terms of AP

Let the first term and common difference of an AP containing n terms be a and d, respectively.

Let T_n be the last term of an AP.

Then, the sum of n terms of the AP is

                           S_n=frac{n}{2}[2a+(n-1)d]

                                  =frac{n}{2}[a+T_n]

Illustration 1.  A contract on construction job specifies a penalty for delay in completion of the work beyond a certain data is as follows Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day etc. the penalty for each succeeding day being Rs. 50 more than penalty. What penalty should the contractor pay, if he delays the work by 10 days ?

A. Rs. 4950           B. Rs. 4250            C. Rs. 3600           D. Rs. 650

Answer: B

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Sample Questions
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Question : 1

Find the sum of 20 terms of the A.P. 1,4,7,10...

Right Option : D
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Explanation
 
 
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