Question

If the g.p 162,54,18,...and 2/81,2/27,...have their nth terms equal then find value of n

Answer 1

Answer:

n = 5

Step-by-step explanation:

If the g.p 162,54,18,...and 2/81,2/27,...have their nth terms equal then find value of n

162 , 54 , 18

a = 162  r = 54/162 = 1/3

nth term

= arⁿ⁻¹

= 162(1/3)ⁿ⁻¹

2/81 , 2/27

a = 2/81  r = (2/27)/(2/81) = 3

nth term

= arⁿ⁻¹

= (2/81)(3)ⁿ⁻¹

162(1/3)ⁿ⁻¹  =  (2/81)(3)ⁿ⁻¹

=> 81*81 = (3)ⁿ⁻¹/((1/3)ⁿ⁻¹)

=> 3⁴*3⁴ = 3⁽²⁽ⁿ⁻¹⁾⁾

=> 2(n-1) = 8

=> n - 1 = 4

=> n = 5

5th term would be equal

5th term = 2