Question

which of the following cannot be the general term of an A.P ,4n+3,3n²+5,2n-4/5

Answer 1

(i) 
an = 4n+3

an+1 = 4(n+1)+3

an+1 = 4n+4+3

an+1 = 4n+7

Now an+1 -  an = 4n+7 -4n-3 =  4

So it is a general term.
 
(ii)

3n^2 +5 

an = 3n^2 +5 

an+1 = 3(n+1)^2 +5

an+1 = 3(n2 +1+2n) +5

an+1 = 3n^2 +3 +6n +5

Now an+1 -  an = 3n^2 +6n +8 - 3n^2 -5 = 6n+3

Since it not independent of n it is not a general term of A.P.

(iii) 
an = 2n -   4/5

an+1 = 2(n+1) - 4/5
                         
an+1 = 2n +2 - 4/5

Now an+1 -  an = 

2n +2 - 4/5   -  2n +  4 /5

= 2

Hence it is also a general term.

So , Second term 3n^2 +5 is not the general term of A.P.