Write the general term of a G.P.

1.	Write the general term of a G.P.
Answer» Let a be the first term and (r ≠ 0) be the common ratio of a G.P. Then general term of G.P.is T_n= a . r^n-1 Note: Terms in G.P.are in the form a, ar, ar² , ar^n-1, No term in G.P.can be zero. Three terms a,b,c are in G.P. if b/a = c/b i.e b² = ac, abc ≠ 0 The general form of a GP is a, ar, ar², ar³ and so on. The nth term of a GP series is T_n = arⁿ^-¹, where, a = first term and r = common ratio = T_n/T_n_-₁ . The sum of infinite terms of a GP series, S_∞= a/(1-r) where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.

Answer»

Let a be the first term and (r ≠ 0) be the common ratio of a G.P. Then general term of G.P.is T_n= a . r^n-1

Note:

Terms in G.P.are in the form a, ar, ar² , ar^n-1,

No term in G.P.can be zero.

Three terms a,b,c are in G.P.

if b/a = c/b i.e b² = ac, abc ≠ 0

The general form of a GP is a, ar, ar², ar³ and so on. The nth term of a GP series is

T_n = arⁿ^-¹,

where, a = first term and r = common ratio = T_n/T_n_-₁ .

The sum of infinite terms of a GP series, S_∞= a/(1-r)

where 0< r<1. If a is the first term, r is the common ratio of a finite G.P.

Discussion