Question

Sequence and Series question???????

Answer 1

If a,b,c are in AP and a^2,b^2,c^2 are in GP a<b<c and a+b+c=3/2 then value of a is

Answer 2

@ganeshie8 @ikram002p hlp

Answer 3

what is AP and GP?

Answer 4

Arithmetic and Geometric Progression?

Answer 5

Aritmetic Progression and Geometric Progession

Answer 6

yes

Answer 7

b=1/2

Answer 8

found out

Answer 9

a??????

Answer 10

Ok, well if a, b, and c are in an arithmetic progression, then that means there's some quantity you can add to a to get b and to b to get c. Similarly we can set up an equation for their squares in the GP.

Answer 11

YES

Answer 12

So make as many equations as you can and see if we can solve for anything.

Answer 13

well
c-b=b-a
\(c^2/b^2=b^2/a^2\)

Answer 14

yes

Answer 15

ok
c+a-2b=0
2a+2b+2c=3

\(c^2 a^2=b^4\)

\(ca=b^2\)


ok u have 3 equations with 3 variables ^
solve

Answer 16

i have solved it this like but the answer is wrong

Answer 17

@ikram002p @Kainui @hartnn view this answer is \[\frac{ 1 }{2 }-\frac{ 1 }{ \sqrt{2} }\]

Answer 18

pls hlp

Answer 19

ac = 1/4
a+c = 2b =1

Answer 20

quadratic in a

Answer 21

yes i did this

Answer 22

c=2,a=-1

Answer 23

getting
a=b=c= 1/2 ...which are not acceptable values

Answer 24

no i got a=-1,b=1/2,c=2

Answer 25

b^4 = (ac)^2

b^2 = +ac, b^2 =-ac

ac = -1/4

Answer 26

yeah

Answer 27

ac =-1/4
a+c =1/2

now you will get it

Answer 28

a-1/(4a) = 1/2
solve

Answer 29

I am getting the same too. a = b = c = 1/2. Satisfies all equations except they AP and GP unless a common difference of zero counts as AP and common ratio of 1 counts as GP.

Answer 30

ok so i didn't +- ok

Answer 31

doesn't satisfy a<b<c aum

Answer 32

Oh, yeah. Some mistake in this problem? or a typo?

Answer 33

yes @hartnn u r cprrect @aum 1/2 is not the answer

Answer 34

no mistake

a-1/(4a) = 1/2
did u get how i got this equation

Answer 35

yes @hartnn

Answer 36

solve it, its a quadratic

Answer 37

sorry, that should be
a-1/(4a) = 1

because
a+c = 2b =1

Answer 38

@hartnn is righttt..btw hartnn cud u help me out

Answer 39

i got \[4a^2-4a+1\]

Answer 40

a+c = 2b =1
ac = -b^2 , ac = b^2

ac =b^2 is rejected because a<b<c

ac=-b^2 =-1/4

Answer 41

you should get
4a^2 -4a-1 =0

Answer 42

wait let me check and figyre out ny nistake

Answer 43

ok

Answer 44

i didn't reject +b^2

Answer 45

got u hartnn

Answer 46

4a^2 -4a-1 =0
will give you one root as your answer

Answer 47

got it