Question

9.1,-а, а-азn terms (ifa #-1)

Answer 1

The G.P. is 1,−a, a 2 ,− a 3 ,…

Let the first term and common ratio of the given G.P. be a 1 and r respectively.

Here,

a 1 =1 r= −a 1 =−a

Here, r<1

The formula for the sum of first n terms of a G.P. for r<1 is given by,

S n = a 1 ( 1− r n ) 1−r

Substitute the values of a 1 and rin equation (1) to obtain the n th term.

S n = 1×( 1− ( −a ) n ) 1−( −a ) = 1×( 1− ( −a ) n ) 1+a

Thus, the sum of n terms of the G.P. 1,−a, a 2 ,− a 3 ,… is 1×( 1− ( −a ) n ) 1+a .