Find Sum of N Terms When A.P. and Last Term is Given


 
 
Concept Explanation
 

Find Sum of N Terms When A.P. and Last Term is Given

Sum of N Terms When First Term, Last Term is Given: The sum can be found by using the formula.

large _{S_{n}}=frac{n}{2}(a+l)

For using this formula we will first find the number of terms

Example :    Find the sum for the given A.P.  34+ 32+ 30+....+10

Solution:   Here, the last term is given. We will first have to find the number of terms.

 large a = 34,d=32-34=-2,l=a_{n}=10

   large therefore  large 10 = a+(n-1)d

  large Rightarrow 10 =34+(n-1)(-2)

  large Rightarrow (-2)(n-1)=10-34

  large Rightarrow (-2)(n-1)=-24

  large Rightarrow(n-1)=12Rightarrow n=12+1=13

Using large _{S_{n}}=frac{n}{2}(a+l) We have

large _{S_{13}}=frac{13}{2}(34+10)=frac{13}{2}times 44=13times 22=286

Sample Questions
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Question : 1

Which of the following values is the sum of the AP : 2, 4, 6,..........200? 

Right Option : C
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Explanation
Question : 2

If the last term, number of terms and the sum of all the terms of an AP are 152, 31 and 2387 respectively,  its first term is ________________-

Right Option : A
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Explanation
Question : 3

If the first term, the last term and the sum of all the terms of an AP are 14, 62 and 646 respectively the number or terms in the AP is 

Right Option : B
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Explanation
 
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