Nth Term of AP


 
 
Concept Explanation
 

Finding Nth Term when an AP is Given

Finding Nth Term When an AP is Given:To find the nth term we will use the formula for the nth term of an AP.

a_n=a+(n-1)d

Example:  Find the 10th term of the AP : 2, 7, 12,.....

Solution :    Here,  large a_1=2    and   large n=10.

d_1=a_2-a_1=7-2=5

d_2=a_3-a_2=12-7=5

as d_1=d_2

So the common difference = 5

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

So,                         large a_{10}=2+(10-1)times 5=2+45=47

Therefore , the 10th term of the given AP is 47.

Example: A person invested a sum of Rs 500. After each month 50 Rs are added to the sum. How much money he get after 6 months?

Solution: As Rs 50 are being added each month so the common difference = 50

Fisr term large a_1=500

n= 6 

large a_n= a_1+ (n-1)d

large a_6= 500+ (6-1)50

        large = 500+ (5)50

        large = 500+ 250

        large = 750;Rs

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

For an AP the first term and the common difference are 41 and - 41 respectively the 7^{th} term of the AP is ______________

Right Option : C
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Explanation
Question : 2

If an AP has its first term -5 and common difference 1,  which of the following strings of numbers represents the next four terms of  the AP?

Right Option : C
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Explanation
Question : 3

Which of the following numbers is the 8th term of an AP 13, 26, 39, 52,______________?

Right Option : A
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Explanation
 
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