Download App

Geometric Progressions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsGeometric Progressions3 Marks
Question
If $\frac{1}{\text{a}+\text{b}},\frac{1}{2\text{b}},\frac{1}{\text{b}+\text{c}}$ are three consecutive terms ofan A.P., prove that a, b, c are the three consecutive terms of a G.P.
✓

Answer

$\frac{1}{\text{a}+\text{b}},\frac{1}{2\text{b}},\frac{1}{\text{b}+\text{c}}\text{ are in A.P.}$
$\frac{2}{2\text{b}}=\frac{1}{(\text{a}+\text{b})}+\frac{1}{(\text{b}+\text{c})}$
$\frac{1}{\text{b}}=\frac{\text{b}+\text{c}+\text{a}+\text{b}}{(\text{a}+\text{b})(\text{b}+\text{c})}$
$\frac{1}{\text{b}}=\frac{2\text{b}+\text{c}+\text{a}}{\text{ab}+\text{ac}+\text{b}^2+\text{bc}}$
$\text{ab}+\text{ac}+\text{b}^2+\text{bc}=2\text{b}^2+\text{bc}+\text{ba}$
$\text{b}^2+\text{ac}=2\text{b}^2$
$\text{b}^2=\text{ac}$
So,
a, b, c are in G.P.

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

More "3 Marks Question" from Geometric Progressions→Geometric Progressions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the point in yz-plane which is equidistant from the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).
→
Using binomial theorem write down the expansions of the following:
$\bigg(\sqrt\frac{\text{x}}{\text{a}}-\sqrt\frac{\text{a}}{\text{x}}\bigg)^6$
→
The means and standard deviations of heights ans weights of 50 students of a class are as follows:
  Weights Heights
Mean 63.2kg 63.2 inch
Standard deviation 5.6kg 11.5 inch
Which shows more variability, heights or weights?
→
Show that a real value of $x$ will satisfy the equation $\frac{1-i x}{1+i x}=a-i$ if $a ^2+ b ^2=1$ where $a$ and $b$ are real
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{\text{x}-\text{a}}$
→
In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
How many drink coffee but not tea.
→
If ${^\text{2n}}\text{C}_{\text{3}}:{^\text{n}}\text{C}_{\text{2}}=44:3,$ find n.
→
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box$,$ if atleast one black ball is to be included in the draw.
$[$Hint: Required number of ways $=\ ^3C_1\times ^6C_2+ ^3C_2 \times ^6C_2 + ^3C_3 .]$
→
A sports team of $11$ students is to be constituted$,$ choosing at least $5$ from Class $XI$ and atleast $5$ from Class $XII$. If there are $20$ students in each of these classes$,$ in how many ways can the team be constituted?
→
Check the validity of the statements given below by the method given against it.
q: If n is a real number with $n > 3$, then $n2 > 9$ (by contradiction method).
→