Question

The numbers 3, x and x + 6 form are in G.P.
Find (i) x, (ii) 20th term (iii) n'th term. please answer immediately​

Answer 1

Answer:

x=6

nth term= 3 x 2^(n-1)

20th term = 3 x 2^(19)

Step-by-step explanation:

common ratio is always constant.

r= second term/first term = x/3

similarly,

r= third term/second term = (x+6)/x

thus x/3=(x+6)/x

=x^2=3x+18

x^2-3x-18=0

x^2-(6-3)x-18

x^2-6x+3x-18

x(x-6)+3(x-6)

(x+3)(x-6)

x=-3 or +6

thus x is +6

series is 3, 6, 12

and common ratio R= 2

since a=3

nth term is given by ar^(n-1)

thus 20th term is 3 x 2^(20-1)

= 3 x 2^19

solve it you will get 20th term