Math miscellaneousHard

Question

If a1, a2, .... , an are in H.P., then the expression a1a2 + a2a3 + .... + an-1an is equal to

Options

A.n(a1 - an)
B.(n - 1) (a1 - an)
C.na1an
D.(n - 1)na1an

Solution

= d (say)
Then a1a2 = , a2a3 = , ....., an-1an =
∴     a1a2 + a2a3 + .... an-1an = Also, + (n - 1)d
⇒     = (n - 1)a1an

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