Find The Value of Common Difference when Nth Term, Number of Terms and First Term are Given


 
 
Concept Explanation
 

Find The Value of Common Difference when Nth Term, Number of Terms and First Term are Given

Find The Value of Commom Difference When Nth Term, N and the Fist Term Is Given.: We will use the formula for the general term. Putting the value of n , a and Nth Term we will find d.

Example:  Find the common diffrenece when the first term of an AP is 3 the 16th term of the AP is 78.

Solution :    Here, a= 3, n= 16 and a_n=78

We have                large a_{n}=a+(n-1)d

So,                         large a_{16}=3+(16-1)times d

                                  78 = 3+15 X d

                                  15d = 75

                                    d = 5

Therefore , the common difference d= 5.

Example: Distance between Ambala and Delhi is 200 Km. A person started from Ambala and  traveled 50 Km on the fisrt day. How much Km shoul he travel daily so than he reaches Delhi in 16 days.

Solution: a= 50

                d= ?

                n= 16

               a_n=200

large a_{n}=a+(n-1)d

200=50+(16-1)times d

150=15d

d= 10 Km

He has to travel 10 Km daily.

Sample Questions
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Question : 1

For an AP, the first and the large {15^t^h} term are 7 and -21, respectively. The common difference of the AP is ___________

Right Option : C
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Explanation
Question : 2

For an AP, the first and the large {11^t^h} term are large frac{3}{2} and large frac{23}{2}, respectively. The common difference of the AP is _____________

Right Option : B
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Explanation
Question : 3

For an AP ,the 11th term is 41 and the first term is 11. The common difference of the AP is _______________

Right Option : B
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Explanation
 
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