Question

12. 5th,8th, and 11th terms of a G.P. arep, q and s respectively, prove that q²? = ps. ​

Answer 1

Step-by-step explanation:

Show that q2 = ps. Let a be the first term and r be the common ratio of the G.P. Thus, the given result is proved.

Answer 2

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Given that:

5th term = P

8th term = q

11th term = s

To prove that: q^2 = ps

By using the above information, we can write the equation as:

a5 = ar5-1 = ar4 = p ….(1)

a8 = ar8-1 = ar7 = q ….(2)

a11 = ar11-1 = ar10 =s …(3)

Divide the equation (2) by (1), we get

r^3 = q/p …(4)

Divide the equation (3) by (2), we get

r^3 = s/q …(5)

Now, equate the equation (4) and (5), we get

q/p = s/q

It becomes, q^2 = ps

Hence proved.