Application of DerivativeHard
Question
If the (m + 1)th . (n + 1)th & (r + 1)th terms of an AP are in GP & m, n, r are in HP, then the ratio of the common difference to the first term of the AP is -
Options
A.
B.
C.
D.none of these
Solution
⇒ 
⇒
= x
⇒ (1 + nx)2 = (1 + rx) (1 + mx)
⇒ (n2 - mr)x2 + (2n - r - m)x = 0 ⇒ x = 0
or x =
(m, n, r are in H.P. ⇒ mr =
)
⇒
= x⇒ (1 + nx)2 = (1 + rx) (1 + mx)
⇒ (n2 - mr)x2 + (2n - r - m)x = 0 ⇒ x = 0
or x =
(m, n, r are in H.P. ⇒ mr =
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