If ar$$0$$,r∈N and $$a1$$,$$a2$$,$$a3$$….$$a2n$$ are A.P. then $$a1+a2na1+a2+a2+a2n$$−$$1a2+a3+a3+a2n$$−$$2a3+a4+$$…..$$+an+an+1an+an+1=$$

Question

If ar>$$0$$,r∈N and $$a1$$,$$a2$$,$$a3$$….$$a2n$$ are A.P. then $$a1+a2na1+a2+a2+a2n$$−$$1a2+a3+a3+a2n$$−$$2a3+a4+$$…..$$+an+an+1an+an+1=$$

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$$a1+a2n=a2+a2n$$−$$1$$......$$=K$$ (say) $$a1+a2na1+a2+$$.......$$+an+an+1an+an+1=Ka1$$−$$a2a1$$−$$a2+$$….$$+an$$−$$an+1an$$−$$an+1$$                                                         $$=$$−$$Kda1$$−$$an+1a1+an+1$$   Where $$d=a1$$−$$a2=$$…..$$=an$$−an−$$1$$                                                         $$=na1+a2na1+an+1$$

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If ar>0,r∈N and a1,a2,a3….a2n are A.P. then a1+a2na1+a2+a2+a2n−1a2+a3+a3+a2n−2a3+a4+…..+an+an+1an+an+1=

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