Question

If the (a+1) th , 7th , and (b+1) th terms of an A.P are in G.P with a ,6 , b being in H.P then 4th term of this A.p is?

Answer 1

Can you rewrite this without abbreviations?

Answer 2

it should be there to denote the term "th"

Answer 3

lol...i cant understand what this question says !!

Answer 4

i am getting answer as 0 !!....do u have options??? @Yahoo!

Answer 5

The answer should be 0

Answer 6

Yup u r correct

Answer 7

Can u show that @hartnn

Answer 8

Quite simple if u have tried:
3(a+b)=ab......HP condition
let A be 1st term.,D be common difference
'n'th term is A+(n-1)D
so,GP condition gives
(2A+6D)^2=(2A+aD)(2A+bD)
4A^2 +36D^2+24AD=4A^2+abD^2+2AD(a+b)
on simplifying this,
(36-ab)D=2A(a+b-12)
then use HP condition
so that 36-ab cancels out on both sides
and what remains is -3D=2A--->4th term=0

Answer 9

i tried lol!

Answer 10

now u got it? @Yahoo!

Answer 11

,GP condition gives
(2A+6D)^2=(2A+aD)(2A+bD)???????

Answer 12

b^2 = ac

Answer 13

t7 = a + 6d

Answer 14

u have taken it as 2A

Answer 15

@hartnn r u there

Answer 16

oh my mistake,i am reconsidering now,and will reply u very soon

Answer 17

ok

Answer 18

so,GP condition gives
(A+6D)^2=(A+aD)(A+bD)
A^2 +36D^2+12AD=A^2+abD^2+AD(a+b)
on simplifying this,
(36-ab)D=A(a+b-12)
then use HP condition
so that 36-ab cancels out on both sides
and what remains is -3D=A--->4th term=0

sorry for previous mistake,still i get 4th term=0 :P

Answer 19

HP condition = 3(a+b)=ab

Answer 20

hw did u use that

Answer 21

ok...i got it

Answer 22

thxxx @hartnn