If an arithmetic progression & a geometric progression have the same first term, the last term & the same number of terms, prove that [ . . . ] (see description)?

Question

... the product of the #r^(th)# term from the beginning in one series & the #r^(th)# term from the end in the other is independent of r?

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Answer 1 · 2017-08-29T21:06:49

The claim is false.

Counter-example

A.P: 1, 3, 5, 7, 9 = #a_1, a_2, a_3, a_4, a_5#

G.P: 1, #sqrt3#, 3, #3sqrt3#, 9 #g_1, g_2, g_3, g_4, g_5#

#g_4 a_2 != g_3 a_3 != g_2 a_4#