Home > Precalculus > Sums of Geometric Sequences

Find 5 geometric mean between 1 and 27?

Answer 1

Five geometric mean between #1# and #27# are #sqrt3,3,3sqrt3,9,9sqrt3#

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

#1,a,b,c,d,e,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=3^3=(sqrt3)^6#

and hence #r=sqrt3#

and five geometric mean between #1# and #27# are

#sqrt3,3,3sqrt3,9,9sqrt3#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Liam Brennan

To find the geometric means between 1 and 27, we first calculate the ratio of 27 to 1, which is (27 / 1 = 27). Then, we divide this ratio by the number of geometric means we want plus 1, which is 5 + 1 = 6. So, (27 / 6 = 4.5). Then, we multiply 1 by the successive powers of 4.5 to find the geometric means. The geometric means between 1 and 27 are: 4.5, 4.5 * 4.5, 4.5 * (4.5)^2, 4.5 * (4.5)^3, 4.5 * (4.5)^4, and 27.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.