The numbers x – 6, 2x and x2 are in G. P. Find(i) x(ii) 1st term(iii

1.	The numbers x – 6, 2x and x2 are in G. P. Find(i) x(ii) 1st term(iii) nth term
Answer» (i) x – 6, 2x and x are in Geometric progression. \(\therefore\) \(\frac{2x}{x-6}=\frac{x^2}{2x}\) 4x = x² (x – 6) 4 = x – 6 x = 10 (ii) t₁ = x – 6 = 10 – 6 = 4 (iii) a = 4, r = 2x/(x - 6) = \(\frac{2(10)}4=5\) t_n = ar^n-1 \(\therefore\) t_n = 4(5^n-1)

The numbers x – 6, 2x and x2 are in G. P. Find(i) x(ii) 1st term(iii) nth term

Answer»

(i) x – 6, 2x and x are in Geometric progression.

\(\therefore\) \(\frac{2x}{x-6}=\frac{x^2}{2x}\)

4x = x² (x – 6)

4 = x – 6

x = 10

(ii) t₁ = x – 6 = 10 – 6 = 4

(iii) a = 4, r = 2x/(x - 6) = \(\frac{2(10)}4=5\)

t_n = ar^n-1

\(\therefore\) t_n = 4(5^n-1)