Find Common Difference when First Term, Number of Terms and Sum of N Terms is Given


 
 
Concept Explanation
 

Find Common Difference when First Term, Number of Terms and Sum of N Terms is Given

Find The Common Difference When First Term, Number of Terms and Sum of N Terms is given:

In these type of problems we will use the formula

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

will find the value of d ( Common Difference) by substituting the value of  a (the first term), n(number of terms) and S_n ( Sum of n term) in the equation.

For Example: Find the common difference of an AP whose first term is -3 number of terms is 15 and sum is 60

Solution:       large a = -3,;n= 15; S_n=60

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

Substituting the value of a, n, large s_{n}

large 60= frac{15}{2} left [ 2times (-3)+ (15-1) d right ]

large 60= frac{15}{2} left [ (-6)+ 14d right ]

large 60= frac{15}{2}; X; 2 left [ -3+ 7d right ]

large 60=15 left [ -3+ 7d right ]

large 4= -3+ 7d

7= 7d

d= 1

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 sum of the first 7 terms of the AP is 210 and its first term is 27 the common difference is _____________

Right Option : B
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Explanation
Question : 2

If the sum of the first five terms of an AP is 450 and its first term is 64, its common difference is ______________

Right Option : A
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Explanation
Question : 3

What will be the common difference of the Arithmetic Progression, whose sum of first m terms is given by large 2(m^2+3m) ?

Right Option : B
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Explanation
 
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