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

If the last term ,  the numbers of terms and the sum of all the terms of an AP are 53, 17, 493 respectively. Then its first term is ________________

Right Option : B
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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

Which the following values is the sum of the AP :  3, 0, -3,  -6,  -9, .......  -27? 

Right Option : C
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Explanation
 
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