- Home
- Standard 11
- Mathematics
8. Sequences and Series
medium
$3$ અને $81$ વચ્ચે બે સંખ્યામાં ઉમેરો કે જેથી બનતી શ્રેણી સમગુણોત્તર હોય.
A
$9,27$
B
$9,27$
C
$9,27$
D
$9,27$
Solution
Let $G_{1}$ and $G_{2}$ be two numbers between $3$ and $81$ such that the series, $3, G_{1}, G_{2}, 81,$ forms a $G.P.$
Let $a$ be the first term and $r$ be the common ratio of the $G.P.$
$\therefore 81=(3)(r)^{3}$
$\Rightarrow r^{3}=27$
$\therefore r=3$ (Talking real roots only)
For $r=3$
$G_{1}=a r=(3)(3)=9$
$G_{2}=a r^{2}=(3)(3)^{2}=27$
Thus, the required two numbers are $9$ and $27$
Standard 11
Mathematics
