If a, b, c are in A. P. then 1/bc' 1/ca' 1/ab
are in...........
Answers
Answer :
AP(Arithmetic Progression)
Note :
★ A.P. (Arithmetic Progression) : A sequence in which the difference between the consecutive terms are equal is said to be in A.P.
★ If a1 , a2 , a3 , . . . , an are in AP , then
a2 - a1 = a3 - a2 = a4 - a3 = . . .
★ The common difference of an AP is given by ; d = a(n) - a(n-1) .
★ The nth term of an AP is given by ;
a(n) = a1 + (n - 1)d .
★ If a , b , c are in AP , then 2b = a + c .
★ The sum of nth terms of an AP is given by ; S(n) = (n/2)×[ 2a + (n - 1)d ] .
★ The nth term of an AP can be also given by ; a(n) = S(n) - S(n-1) .
★ A linear polynomial in variable n always represents the nth term of an AP .
★ A quadratic polynomial in variable n always represents the sum of n terms of an AP .
★ If each terms of an AP is multiplied or divided by same quantity , then the resulting sequence is an AP .
★ If same quantity is added or subtracted in each term of an AP then the resulting sequence is an AP .
Solution :
Here ,
It is given that a , b , c are in AP .
Thus ,
=> a , b , c are in AP .
=> a/abc , b/abc , c/abc are in AP .
If each terms of an AP is divided by same quantity , then the resulting sequence is an AP .
Here , each term is divided by abc .
=> 1/bc , 1/ca , 1/ab are in AP .