Question

The numbers 3, x and x + 6 are in G. P. Find

(i) x

(ii) 20th term

(iii) nth term.

Answer 1

(i) 3, x and x + 6 are in G. P.

\(\frac{x}3=\frac{x+6}x\) 

x² = 3x + 18

x² – 3x – 18 = 0

(x – 6) (x + 3) = 0

x = 6, -3

(ii) r = 6/3 = 2 or r = -3/3 = -1

t_n = ar^n-1

(iii) t_n = 3(2)^n-1 or t_n = 3(-1)^n-1