Q3 of 176 Page 21

If and x are in G.P., then write the value of x.

We know when three terms say a,b,c are in GP

We can write

b² = a.c

∴ According to the given data

We can write

(a^x/2)² = log_xa . log_bx

a^x = log_xa . log_bx

⇒

⇒ a^x = log_ba

Multiplying by log_a to both sides we get

⇒ log_a (a^x) = log_a (log_ba)

⇒ x log_aa = log_a (log_ba)

⇒ x = log_a (log_ba)

If the fifth term of a G.P. is 2, then write the product of its 9 terms.

If and terms of a G.P. are m and n respectively, then write its pth term.

If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is , then write its first term and common difference.

If and terms of a G.P. are x, y, z respectively, then write the value of .