The two geometric means between the numbers 1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the two geometric means between $1$ and $64$ be $a$ and $b$.Then the sequence $1, a, b, 64$ forms a Geometric Progression $(GP)$.Let the commo

Vedclass · Accepted Answer

$4$ and $16$

Vedclass · Answer

(B) Let the two geometric means between $1$ and $64$ be $a$ and $b$.Then the sequence $1, a, b, 64$ forms a Geometric Progression $(GP)$.Let the common ratio be $r$.Then $a = 1 \cdot r$,$b = 1 \cdot r^2$,and $64 = 1 \cdot r^3$.From $r^3 = 64$,we get $r = \sqrt[3]{64} = 4$.Therefore,$a = 1 \cdot 4 = 4$ and $b = 1 \cdot 4^2 = 16$.Thus,the two geometric means are $4$ and $16$.

The two geometric means between the numbers $1$ and $64$ are

Similar Questions

If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

The value of $1^2 + 3^2 + 5^2 + ....... + 25^2$ is

Find the sum of all integers between $50$ and $500$ which are divisible by $7.$

If the first,second and last terms of an $A.P.$ are $a, b, 2a$ respectively,then its sum will be

If $\sum\limits_{i = 1}^{20} {\left( {\frac{{{}^{20}{C_{i - 1}}}}{{{}^{20}{C_i} + {}^{20}{C_{i - 1}}}}} \right)} ^3 = \frac{k}{21}$,then $k$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module