There are three numbers a, b, c in g.P. Such that a + b + c = 14. If a and b are increased by 1 and c is decreased by 1 then the series formed by these numbers is in
a.P. Calculate the value for a*b*c ?
Answers
Answer:
a*b*c = 64
Step-by-step explanation:
There are three numbers a, b, c in g.P. Such that a + b + c = 14. If a and b are increased by 1 and c is decreased by 1 then the series formed by these numbers is in a.P. Calculate the value for a*b*c
abc are in GP
=> b² = ac
a + 1 , b + 1 , c - 1 are in AP
=> (a + 1 + c - 1) = 2(b + 1)
=> a +c = 2(b + 1)
a + b + c = 14
=> a + c = 14 - b
=> 14 - b = 2(b + 1)
=> 14 - b = 2b + 2
=> 12 = 3b
=> b = 4
b² = 16
ac = 16
a*b*c = ac * b = 16 * 4 = 64
a*b*c = 64
GP : 2 , 4 , 8 or 8 , 4 , 2
AP 3 , 5 , 7 or 9 , 5 , 1
Answer:
64
Step-by-step explanation:
we have,
a + b + c = 14 -------------- 1
It is clearly mentioned a,b,c are in GP, we get
b^2 = a * c ----------- 2
a + 1, b + 1, c - 1 are in AP. They are only three terms.
second term - first term = Third term - second term
( b+1) - (a+1) = (c-1) - ( b+1)
2*b + 2 = a + c
from equation 1, we get
2*b + 2 = 14 - b
b = 12 /3 = 4.
we got b = 4.
Now,
a ,b c in GP. b * b = a * c
a must be lesser than b.
c must be greater than b.
4 * 4 = a * c
using above statements we can clearly guess that a = 2 and c = 8.
Because these are the only two numbers who will follow the rule of GP.
Hence,
a = 2, b = 4, c = 8
Finally,
a * b * c = 2 * 4 * 8 = 64.
Note - This is Mcq based question. So, we should make answer as soon as possible. We are not suppose to follow every step of solution.
Thanks.