the nth term of an A.P is 3n - 8 . Is the pattern the pattern of numbers so formed in an A.P? If so then find its 16th term.

Dear Student,

Please find below the solution to the asked query:

Given : The n^th term of an A.P is 3n - 8 , So

First term =  a  =  3 ( 1 ) - 8 = 3 - 8 = - 5

Second term  = 3 ( 2 ) - 8 = 6 - 8 = - 2

Third term  = 3 ( 3 ) - 8 = 9 - 8 = 1 

Our A.P. =  - 5 , - 2 , 1 , . . .

So,

Common difference  =  d = ( - 2 ) - ( - 5 ) = - 2 + 5 = 3 , 1 - ( - 2 ) = 1 + 2 = 3

We know formula of n^th term is =  T_n = a + ( n - 1 ) d

Then  ,

16^th term =  - 5 + ( 16 - 1 ) ( 3 ) =   - 5 + ( 15 ) ( 3 ) = - 5 + 45 = 40                                          ( Ans )


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