Nth Term of AP


 
 
Concept Explanation
 

Nth Term of an AP

The nth term of an AP is

T_n=a+(n-1)d

Illustration 1. Find the fifteenth term of the AP - 3, - 9, - 15, ...

- 87           B  -84            C. -88           D. -90

Answer: A

Solution:  in the given series -3, -9,-15

The difference between second and first term is

-9 -(-3) = -9 + 3 = -6

The difference between third and second term is

-15 -(-9) = -15 + 9 = -6

Thus  here

 a = -3, d = -9 - (-3) = - 6 and n = 15

The formula to find the nth term is

 T_n=a+(n-1)d

Substituting the values, we get

therefore    T_1_5 = -3 + (14) (-6)

              = -3 + (14) (-6)

              = -3 + (-84)

             = -87

Hence the correct option is A

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Sample Questions
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Question : 1

Determine the number of terms in the A.P.3,7,11,...407. Also ,find its 20th term from the end .

Right Option : B
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