Q13 of 176 Page 21

The 4th term of a G.P. is square of its second term, and the first term is -3. Find its 7th term.

a = -1

T₄ = (T₂)²

T_n = ar^n-1

∴ a.r³ = (ar)²

r³ = a.r²

⇒ r = a

∴ r =-1

T₇ = ar^7-1

= (-1).r⁶

= -1.(-1)⁶

= -1.

If the G.P.’s 5, 10, 20, …. And 1280, 640, 320, … have their nth terms equal, find the value of n.

If 5^th, 8^th and 11^th terms of a G.P. are p, q and s respectively, prove that a² = ps.

In a GP the 3^rd term is 24, and the 6^th term is 192. Find the 10^th term.

If a, b, c, d and p are different real numbers such that :

(a² + b² + c²)p² – 2(ab + bc + cd) p + (b² + c² + d²) ≤ 0, then show that a, b, c and d are in G.P.