Question

. If a, b, c are in A. P. then a2 (b+c), b2 (с + а), с2 (a + b) are in......​

Answer 1

Answer :

AP(Arithmetic Progression)

Solution :

Please refer to the attachment .

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 .