Finding The Value of N When Nth Term and AP is Given


 
 
Concept Explanation
 

Finding The Value of N When Nth Term and AP is Given

Finding The Value of N when Nth Term and AP is Given: To find the value of N we will first find the common difference and will then use the formula for the general term.

Example : Which term of the AP : 21, 18, 15,.....is- 81? Also, is any term 0? Give reason for your answer.

Solution :   Here, a= 21  and   large a_{n}=-81, and we have to find n.

d_1=a_2-a_1=18-21=-3

d_2=a_3-a_2=15-18=-3

as d_1=d_2

So the common difference = -3

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

we have             large -81=21+(n-1)(-3)

                          large -81=24-3n

                           large -105=-3n

So,                         large n=35

Therefore, the 35th term of the given AP is -81

Next, we want to know if there is any n for which large a_{n}=0.  If such an n is there, then

                        large 21+(n-1)(-3)=0,

i.e.,                               large 3(n-1)=21

i.e.,                                       large n=8

So, the eighth term is 0.

 

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

For an AP, the first term is 17, common difference is - 4 and  the nth term is - 3. Which of the following numbers represents the value of n?

Right Option : C
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Explanation
Question : 2

For an AP the first term is -1 the common difference is -1 and the n^{th} term is -11. Which of the following numbers represents the value of n?

Right Option : B
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Explanation
Question : 3

For an AP the first term is 7, the common difference is 5 and the n^{th} term is 67 . Which of the following numbers represents the value of n?

Right Option : B
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Explanation
 
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