Question

the 4th term of aG.P is 2/3 and the 7th term is 16/81.find the geometric series

Answer 1

Answer:

G.p. series   ⇒  9/4,27/8,81/16,243/32 .........

Step-by-step explanation:

Let the 1st term be a and common ratio is r,

Fourth term :-

ar^3=2/3           .......(1)

Seventh term:-

ar^6=16/81     .......(2)

Dividing  equation  1st by 2nd we get ;

r^3=(2/3)/(16/81)

r^3=27/8

  So ,r^3=(3)^3/(2)^3

r=3/2

Put the value of  r in any eq. and find the value of a

a*(3/2)^3=2/3

a=9/4

G.P. series ⇒ a,ar,ar^2,ar^3 ..........ar^n-1.

  G.p. series   ⇒  9/4,27/8,81/16,243/32 ....................