If five G.M.’s are inserted between 486 and 2/3 then fourth G.M. … - Vidyadip

Question

If five $G.M.’s$ are inserted between $486$ and $2/3$ then fourth $G.M.$ will be

✓

Answer

b
(b) Let ${G_1},{G_2},{G_3},{G_4},{G_5}$ be the $G.M.’s$ are inserted between $486$ and $2/3$.

So total terms are $7$.

${T_n} = a{r^{n - 1}}$

==> $2/3 = 486$${(r)^6}$

$ \Rightarrow r = 1/3$

Hence $4^{th}$ $G.M.$ will be,

${T_5} = a{r^4} = 486\,{(1/3)^4} = 6$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The graph of the conic $ x^2 - (y - 1)^2 = 1$ has one tangent line with positive slope that passes through the origin. the point of tangency being $(a, b). $ Then Length of the latus rectum of the conic is

If $m$ arithmetic means $( A . Ms )$ and three geometric means $(G.Ms)$ are inserted between $3$ and $243$ such that $4^{\text {th }}$ $A.M.$ is equal to $2^{\text {nd }}$ $G.M.$, then $m$ is equal to

A quadrilateral has distinct integer side lengths. If the second-largest side has length $10$, then the maximum possible length of the largest side is

If the function $f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} & ,|x| \geq 2 \\ ax ^2+2 b, & |x|<2\end{array}\right.$ is differentiable on R, then 48 (a + b) is equal to ________.

If $f:R \to R$ and $g:R \to R$ are one to one, real valued functions, then the value of the integral $\int_{\, - \pi }^{\,\pi } {[f(x) + f( - x)]\,[g(x) - g( - x)]\,dx} $ is

If the system of linear equations $x + ky + 3z = 0;3x + ky - 2z = 0$ ; $2x + 4y - 3z = 0$ has a non-zero solution $\left( {x,y,z} \right)$ then $\frac{{xz}}{{{y^2}}} = $. . . . .

Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-

If the locus of the point, whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5: 4$, is $a x^2+b y^2+c x y+d x+e y+170=0$, then the value of $\mathrm{a}^2+2 \mathrm{~b}+3 \mathrm{c}+4 \mathrm{~d}+\mathrm{e}$ is equal to:

The sum of the following series

$1 + 6 + \frac{{9({1^2} + {2^2} + {3^2})}}{7} + \frac{{12({1^2} + {2^2} + {3^2} + {4^2})}}{9} + \frac{{15({1^2} + {2^2} + .... + {5^2})}}{{11}} + ...$ up to $15$ terms, is

How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels