MyQuestionIcon

1

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

Inductive Step

Let a1, a2,...

Question

Let $a_{1}, a_{2}, a_{3}, a_{4}$ be real numbers such that and $a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} = 1$ . Then the smallest possible value of the expression $(a_{1} - a_{2})^{2} + (a_{2} - a_{2})^{2} + (a_{3} - a_{4})^{2} + (a_{4} - a_{1})^{2}$ lies in interval .

A

(0.15, 2)

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

B

(- 1.5, 2.5)

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

C

(2.5, 3)

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

D

(3, 3.5)

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

Open in App

Solution

The correct option is B $(- 1.5, 2.5)$
Smallest value of $(a_{1} - a_{2})^{2} + (a_{2} - a_{3})^{2} + (a_{3} - a_{4})^{2} + (a_{4} - a_{1})^{2}$ is $0$ , when $a_{1} = a_{2} = a_{3} = a_{4} = \frac{1}{2}$ .

Suggest Corrections

thumbs-up

0

Similar questions

a_{1}, a_{2}, a_{3}, a_{4}

be real numbers such that

a_{1} + a_{2} + a_{3} + a_{4} = 0

a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} = 1

. Then the smallest possible value of the expression

(a_{1} - a_{2})^{2} + (a_{2} - a_{3})^{2} + (a_{3} - a_{4})^{2} + (a_{4} - a_{1})^{2}

lies in the interval

a_{1}

a_{2}

a_{3}

a_{4}

b

are real numbers such that

(a_{1}^{2} + a_{2}^{2} + a_{3}^{2}) b^{2} - 2 (a_{1} a_{2} + a_{2} a_{3} + a_{3} a_{4}) b + (a_{2}^{2} + a_{3}^{2} + a_{4}^{2}) \leq 0

a_{1}

a_{2}

a_{3}

a_{4}

are the terms of a/an

a_{1}, a_{2}, a_{3}, \dots

are in A.P. and

a_{1}^{2} - a_{2}^{2} + a_{3}^{2} - a_{4}^{2} + \dots + a_{2 k - 1}^{2} - a_{2 k}^{2}

= M (a_{1}^{2} - a_{2 k}^{2})

Q. Let the sequence

a_{1}, a_{2}, a_{3} . . .

A . P .

then the value of

a_{1}^{2} - a_{2}^{2} + a_{3}^{2} - a_{4}^{2} + \dots + a_{2 n - 1}^{2} - a_{2 n}^{2}

Let the sequence $a_{1}, a_{2}, a_{3} . . . . . a_{n}$ form an A.P. Then
$a_{1}^{2} - a_{2}^{2} + a_{3}^{2} - a_{4}^{2} + . . . . . + a_{2 n - 1}^{2} - a_{2 n}^{2}$ is equal to

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Mathematical Induction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon