let the sequence a1,a2 an form an A P - Maths - Sequences and Series

Question

let the sequence a1,a2 an form an A P Then a1^2 -a2^2 + a3^2 - a4^2
+ - a2n^2 is equal to ???

Ajanta Trivedi · Accepted Answer

the given expression is
a12-a22+a32-a42+ -a2n2=(a1-a2)(a1+a2)+(a3-a4)(a3+a4)+
+(a2n-1-a2n)(a2n-1+a2n)=-d (a1+a2)-d (a3+a4)- -d
(a2n-1+a2n),                          where d is the common difference=-d
a1+a2+a3+a4+ +a2n=-d
S2n  where S2n is the sum of 2n terms of AP
hope this helps you

let the sequence a1,a2.... .an.......form an A.P. . Then a1^2 -a2^2 + a3^2 - a4^2 + .......- a2n^2 is equal to ???