1. Tardigrade
  2. Question
  3. Mathematics
  4. Consider three sequences an A.P., a.G.P. and a H.P. as follows a, A 1, A 2, A 3, ldots ldots . . . . . . . A 9, b (A.P.) a, G 1, G 2, G 3, ldots ldots . . . . . . G 9, b (G.P.) a, H 1, H 2, H 3, ldots ldots . . . . . . . H 9, b (H.P.) If a, b are the roots of the equation x2-(p+1) x+16=0, p ∈ R, then the value of displaystyle prodr=14 Ar H10-r G10-2 r is

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Q. Consider three sequences an A.P., a.G.P. and a H.P. as follows
a, $A _1, A _2, A _3, \ldots \ldots . . . . . . . A _9$, b (A.P.)
a, $G _1, G _2, G _3, \ldots \ldots . . . . . . G _9, b$ (G.P.)
a, $H _1, H _2, H _3, \ldots \ldots . . . . . . . H _9, b$ (H.P.)
If $a, b$ are the roots of the equation $x^2-(p+1) x+16=0, p \in R$, then the value of $\displaystyle\prod_{r=1}^4 A_r H_{10-r} G_{10-2 r}$ is

Sequences and Series

Solution:

Correct answer is (d) $4^{12}$