Q1 of 176 Page 21

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

Given: Fifth term of GP is 2

⇒ Let the first term be a and the common ratio be r.

∴ According to the question,

T₅ = 2

We know,

a_n = ar^n-1

a₅ = a.r^5-1

2 = ar⁴

GP = a,ar,ar²,…,ar⁸

Product required = a×ar×ar²×…×ar⁸

= a⁹.r³⁶

= (ar⁴)⁹

= (2)⁹

= 512

If the A.M. of two positive numbers a and b (a > b) is twice their geometric mean. Prove that : a : b = (2 + ) : (2 – ).

If one A.M., A and two geometric means G₁ and G₂ inserted between any two positive numbers, show that

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

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