Home
Class 12
MATHS
Three non-zero numbers a ,b ,a n dc are ...

Three non-zero numbers `a ,b ,a n dc` are in A.P. Increasing `a` by 1 or increasing `c` by 2, the numbers are in G.P. Then find `bdot`

Text Solution

Verified by Experts

a,b, and c are in A.P. Hence,
2b=a+c (1)
Again by the given condition, a+1,b,and c are in G.P. and a,b, and c+2 are in G.P. Hence,
`b^(2)=(a+1)c` (2)
and `b^(2)=a(c+2)` (3)
By (2) and (3),
(a+1)c=a(c+2)
or ac+c=ac+2a
or c=2a
Equation (2) gives `b^(2)=(a+1)2a`
Also,Eq.(1) gives
`2b=a+2a=3a`
or `b=(3a)/2`
or `(9a^(2))/4=(a+1)2a`
or `(9a)/8=a+1`
or a=8
or c=2(8)=16
`rArr` 2b=8+16=24
or b=12
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 5.43|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 5.44|1 Videos

  • PROGRESSION AND SERIES

    CENGAGE ENGLISH|Exercise ILLUSTRATION 5.41|1 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

The sum of three numbers a ,b ,c in A.P. is 18 . If aa n db are each increased by 4a n dc is increased by 36 , the new numbers form a G.P. Find a ,b ,c

Three numbers, whose sum is 21, are in A.P. If 2, 2, 14 are added to them respectively, the resulting numbers are in G.P. Find the numbers.

If three positive numbers a, b, c are in A.P. and 1/a^2,1/b^2,1/c^2 also in A.P. then

If a,b,c are in A.P. as well as in G.P. then

Three non-zero real numbers from an A.P. and the squares of these numbers taken in same order from a G.P. Then, the number of all possible value of common ratio of the G.P. is

Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is (A) 2-sqrt(3) (B) 2+sqrt(3) (C) sqrt(3)-2 (D) 3+sqrt(2)

Three numbers are in A.P. and their sum is 15. If 1,4 and 19 be added to these numbers respectively the number are in G.P. Find the numbers .

The numbers a,b,c are in A.P. and a+b+c=60 . The numbers (a-2) , b , (c+3) are in G.P. Then which of the following is not the possible value of a^(2)+b^(2)+c^(2) ?

The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers are in A.P. Find the largest of those numbers − smallest of those numbers ?

Three number whose product it 512 are in G.P. If 8 is added to the first and 6 to the second , the number will be in A.P. The numbers are

Home
Profile