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Q.

The sum of the first Question Image terms of an A.P. is S n =3 n 2 +2n  . What will be its 15th term?


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a

70

b

89

c

79

d

68 

answer is B.

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Detailed Solution

Given that the sum of the first n terms of an A.P is S n =3 n 2 +2n  .
The nth term of an arithmetic progression with first term ‘a’ and common difference ‘d’ is a n =a+ n−1 d  .
Taking the values for n   from 1,2,3... and substituting them in the given sum,
When n=1  ,
⇒ S 1 =3 1 2 +2 1 ⇒ S 1 =3+2 ⇒ S 1 =5   Then,
a 1 = S 1 ⇒ a 1 =5  
The first term is a=5  .
 When n=2  ,
⇒ S 2 =3 2 2 +2 2 ⇒ S 2 =12+4 ⇒ S 2 =16   Then,
a 2 = S 2 − S 1 ⇒ a 2 =16−5 ⇒ a 2 =11   The second term is  a 2  = 16.
When n=3  ,
⇒ S 3 =3 3 2 +2 3 ⇒ S 3 =27+6 ⇒ S 3 =33   Then,
a 3 = S 3 − S 2 ⇒ a 3 =33−16 ⇒ a 3 =17   The third term is a 3  = 17.
Therefore, the arithmetic progression will be 5,11,17,... .
Here,
a=5 d= a 2 − a 1 ⇒d=11−5 ⇒d=6  
Substituting a=5, n=15 and d= 6   in the equation a n =a+ n−1 d  ,
⇒ a 15 =5+ 15−1 6 ⇒ a 15 =5+(14×6) ⇒ a 15 =5+84 ⇒ a 15 =89  
Thus the 15th term will be 89.
Therefore the correct option is 2.
 
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