Question

a=1 and any term is equal to the sum of the succeding terms find r in a infinite gp

Answer 1

Geometric series, G. P. = a + ar² + ar³ + ar⁴
.......

Here, a = 1

So, G. P. = r + r² + r³ + r⁴ .......

For infinite G. P.

1 = r / ( 1 - r ).

1 = r / ( 1 - r )

( 1 - r ) = r

1 = r + r = 2r

r = 1 / 2.

⏺️So, r ( common term) of infinite G. P. is 1 / 2.