Geometric Progression

Step 1: Understand the concept of G.P.
(Geometric Progression).
In a geometric progression (G.P.), the

n%5E%7B%5Ctext%7Bth%7D%7D

term is given by:

T_n%20%3D%20ar%5E%7Bn-1%7D

where

a

is the first term and

r

is the common ratio.
Step 2: Use the given information.
Let the first term be

a

and the common ratio be

r

.
We are given that the

(m%20%2B%20n)%5E%7B%5Ctext%7Bth%7D%7D

term is

P

, and the

(m%20-%20n)%5E%7B%5Ctext%7Bth%7D%7D

term is

q

.
Using the formula for the

n%5E%7B%5Ctext%7Bth%7D%7D

term of a G.P., we get the following equations:

T_%7Bm%2Bn%7D%20%3D%20ar%5E%7Bm%2Bn-1%7D%20%3D%20P

T_%7Bm-n%7D%20%3D%20ar%5E%7Bm-n-1%7D%20%3D%20q

Step 3: Find the $m%5E%7B%5Ctext%7Bth%7D%7D$ term.
The

m%5E%7B%5Ctext%7Bth%7D%7D

term is:

T_m%20%3D%20ar%5E%7Bm-1%7D

Now, using the given equations for

P

and

q

, we can solve for

T_m

T_m%20%3D%20%5Csqrt%7BPq%7D

Step 4: Conclusion.
The

m%5E%7B%5Ctext%7Bth%7D%7D

term is

%5Csqrt%7BPq%7D

, which is option (c).

Chapter Questions
1 MCQs