The sum of the series `a-(a+d)+(a+2d)-(a+3d)+` up to `(2n+1)` terms is- a. `-n d`. b. `a+2n d`. c. `a+n d`. d. `2n d`

If sum of the series a- (a+d) + (a+ 2d)- (a + 3d) + ….up to 21 terms is

The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is -nd b.a+2nd c.a+ndd .2nd

The mean deviation of the series a , a+d , a+2d , , a+2n from its mean is ((n+1)d)/(2n+1) (b) (n d)/(2n+1) (c) (n(n+1)d)/(2n+1) (d) ((2n+1)d)/(n(n+1))

Assertion: The sum of 'n' terms of the series 2+8+14+.. is 3n^(2)-n Reason : If the series is an A.P.with c.d.6 the sum of 'n' terms is 3n^(2)-n

Statement-1: The sum of n terms of the series a+(a+d)+(a+2d)+...(a+(n-1)d)=(n)/(2)[2n+(n-1)d] Statement-2:- Mathematical induction is valid only for natural numbers.

Statement-1: The sum of n terms of the series a+(a+d)+(a+2d)+...(a+(n-1)d)=(n)/(2)[2a+(n-1)d] Statement-2:- Mathematical induction is valid only for natural numbers.

In an arithmetic series, the sum of the first 2n terms is half the sum of the first 3n terms. If a = 12 and d = 3, find the value of n.