Question

Find 5 geometric means between 1 and 27.

Answer 1

Note: n th th term of a GP =ar^(n-1)

Answer:

Five geometric mean between 1 and 27 are √3 , 3, 3√3, 9 , 9√3

Explanation:

Let the five geometric mean between 1 and 27be b,c,d, e and f. In other words

1,b,c,d,e,f,27 are in geometric sequence, with first term as 1 and assume common ration is r. Then as 27 is seventh term, we have

1×r^6=27
i.e. r^6=27
r=6✓27=✓3

and hence r=√3

and five geometric mean between 1 and 27 are find out as,
b=2nd term =1×✓3^1=✓3
c=3rd term=1×✓3^2=3
d=4th term=1×✓3^3=3✓3
e=5th term=1×✓3^4=9
f=6th term=1×✓3^5=9✓3

So, five geometric means are,

√3,3,3√3,9,9√3