Sum of First n Terms of AP


 
 
Concept Explanation
 

Sum of First n Terms

Sum of N Terms of an AP: The sum of n terms when the AP is given

 large S_n=large frac{n}{2}left [ 2a+(n-1)d right ];or;=frac{n}{2}(a+l)

When l = Last term up to which the sum of A.P. is to find

For Example: Find the sum of first 10 terms of the given AP 34+ 37+ 40+....

Solution:                       large a = 34,;d=37-34=3;,n=10

 large Rightarrow 34+37+40+.....10 ;terms = ?

 large S_{n}=frac{n}{2}left [ 2a+(n-1) dright ]

Substituting thevalue of 'a' and 'd ' and n  in large s_{n}

large S_n= frac{10}{2} left [ 2times 34+ (10-1) 3 right ]large S_n= frac{10}{2} left [ 68+ (9)3 right ]

large S_n= frac{10}{2} left [ 68+ (9)3 right ]large = 5 left [ 68+ 27 right ]=5 times 95=475

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If the 1st term is equal to the common difference and the 2nd term is 10, the sum of 1st 20 terms is ____________________

Right Option : C
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Question : 2

If large x_1,x_2,x_3,--------x_n are in AP,then the value of large frac{1}{x_1x_2}+frac{1}{x_2x_3}+frac{1}{x_3x_4}+-------frac{1}{x_n-1x_n} is

Right Option : A
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Question : 3

If the sum and the product of 1st 3 terms of an AP Series is 42 and 2240 respectively, what are the terms of the series?

Right Option : B
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Explanation
 
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