Consider a geometric progression (G.P.) in which two of its terms are known.

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Consider a geometric progression (G.P.) in which two of its terms are known. (i) State the general expression for the

n

th term of a G.P. whose first term is

a

and common ratio is

r

. (ii) If the

p

th term is

T_p

and the

q

th term is

T_q

, prove that

\dfrac{T_q}{T_p}=r^{\,q-p}

. (iii) Using the result of part (ii), explain how the values of

a

and

r

can be uniquely determined when

T_p,\,T_q

and the positions

p,\,q

are given with

p\neq q