Tardigrade
Question
Mathematics
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

Q. Consider three sequences an A.P., a.G.P. and a H.P. as follows
a, $A_{1}, A_{2}, A_{3}, \dots\dots ....... A_{9}$ , b (A.P.)
a, $G_{1}, G_{2}, G_{3}, \dots\dots ...... G_{9}, b$ (G.P.)
a, $H_{1}, H_{2}, H_{3}, \dots\dots ....... H_{9}, b$ (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 $r = 1 \prod 4 A_{r} H_{10 - r} G_{10 - 2 r}$ is

92 113 Sequences and Series Report Error

A

16

B

64

C

$4^{9}$

D

$4^{12}$

Solution:

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