MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Arithmetic Mean

If S A =2 m +...

Question

If $S_{A} = 2 m + (2 m + 1) + (2 m + 2) + . . . + 4 m$ and $S_{B} = (2 m + 1) + (2 m + 3) + (2 m + 5) + . . . + (4 m - 1),$ then

A

\frac{S_{A}}{S_{B}} = 2 + \frac{1}{m}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

\frac{S_{A}}{S_{B}} = \frac{4}{3} + \frac{2}{3 m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{S_{A}}{S_{B}} = \frac{4}{3} + \frac{1}{m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{S_{A}}{S_{B}} = \frac{1}{3} + \frac{1}{m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{S_{A}}{S_{B}} = 2 + \frac{1}{m}$
$S_{A} = 2 m + (2 m + 1) + (2 m + 2) + . . . + 4 m$
Number of terms in the series $S_{A}$ is $2 m + 1$
$S_{A} = \frac{2 m + 1}{2} (4 m + 2 m) ∴ S_{A} = 3 m (2 m + 1)$

$S_{B} = (2 m + 1) + (2 m + 3) + . . . + (4 m - 1)$
Number of terms in the series $S_{B}$ is $m$
$S_{B} = \frac{m}{2} [2 m + 1 + 4 m - 1] ∴ S_{B} = 3 m^{2}$

Therefore,
$\frac{S_{A}}{S_{B}} = \frac{2 m + 1}{m} = 2 + \frac{1}{m}$

Suggest Corrections

thumbs-up

1

Similar questions

A = (a t^{2}, 2 a t), B = (\frac{a}{t^{2}}, - \frac{2 a}{t}), S (a, 0)

\frac{1}{S A} + \frac{1}{S B} =

A (a^{2}, 2 a) B (\frac{1}{a^{2}}, \frac{- 2}{a})

and S(1,0) then prove that

\frac{1}{S A} + \frac{1}{S B} = 1

Q. If A (a²,2a) ,B (1/a²,-2/a) and S( 1 ,0 ), then prove that 1/SA +1/SB =1

S_{A} = 2 m + (2 m + 1) + (2 m + 2) + . . . + 4 m

S_{B} = (2 m + 1) + (2 m + 3) + (2 m + 5) + . . . + (4 m - 1),

Q. If a man increases his speed by

2 m / s

, his kinetic energy is doubled. The original speed of the man is

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Arithmetic Mean

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon