If a1,a2,a3,⋯,a2k are in A.P.,Prove that a1^2-a2^2+a3^2-a4^2+⋯+a(2k-1)^2-a2k^2=k/(2k-1)(a1^2-a2k^2)

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Let a1,a2,a3 are AP of positive terms Let a1^2 -a2^2+a3^2-a4^4+....+a2k-1^2-a2k^2=Ak If A3=-153,A5

a1^2 - a2^2 +a2^2- a3^2 ......=k/2k-1(a1^2 -a2k^2) last year iit questions of sequence and series

`(a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)`

Let `a_1,a_2,a_3,......` be an A.P. such that `[a_1+a_2+......+a_p]/[a_1+a_2+a_3+......+a_q]=p^...

prove that ((1+a1+a1^2 )(1+a2+a2^2 )(1+a3+a3^2 )…⋅(1+an+an^2 ))/(a1⋅a2⋅a3..…an )≥ 3^n

If `a_1, a_2, a_3,.....a_n` are in H.P. and `a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1

|a1 + a2 + ... + an| ≤ |a1| + |a2| + ... + |an| (Proof) [ILIEKMATHPHYSICS]

Let \[{a_1},{a_2},{a_3},........\] be in an A.P. such that \[\sum\limits_{k = 1}^{12} {{a_{2k - 1}}}