If the sum of `n` terms of an A.P. is given by `S_n=a+b n+c n^2, w h e r ea ,b ,c` are independent of `n ,t h e n` `a=0` common difference of A.P. must be `2b` common difference of A.P. must be `2c` first term of A.P. is `b+c`

Options

A. a=0
B. common ifferecnce of A.P must be 2 b
C. common difference of A.P must 2c
D. first term of A.P is b+c

Answer

A, C, D

Explanation

`S_(n)=n/2[2a'+(n-1)d]=a+bn+cn^(2)`
`rArrna'+(n(n-1))/2d=a+bn+cn^(2)`
`rArr(a'-d/2)n+(n^(2)d)/2=a+bn+cn^(2)`
On comparing,
a=0,b=a'-`d/2,c=d/2rArrd=2c`