If x_1, x_2, dots, x_n and frac{1}{h_1}, frac | vedclass

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(A) Let $d_1$ be the common difference of the $A.P.$ $x_1, x_2, \dots, x_n$.Given $x_3 = 8$ and $x_8 = 20$.$x_8 - x_3 = (8-3)d_1 = 5d_1 = 20 - 8 = 12

Vedclass · Accepted Answer

$2560$

Vedclass · Answer

(A) Let $d_1$ be the common difference of the $A.P.$ $x_1, x_2, \dots, x_n$.Given $x_3 = 8$ and $x_8 = 20$.$x_8 - x_3 = (8-3)d_1 = 5d_1 = 20 - 8 = 12 \Rightarrow d_1 = \frac{12}{5} = 2.4$.Then $x_5 = x_3 + 2d_1 = 8 + 2(2.4) = 8 + 4.8 = 12.8$.Let $d_2$ be the common difference of the $A.P.$ $\frac{1}{h_1}, \frac{1}{h_2}, \dots, \frac{1}{h_n}$.Given $\frac{1}{h_2} = \frac{1}{8}$ and $\frac{1}{h_7} = \frac{1}{20}$.$\frac{1}{h_7} - \frac{1}{h_2} = (7-2)d_2 = 5d_2 = \frac{1}{20} - \frac{1}{8} = \frac{2-5}{40} = -\frac{3}{40} \Rightarrow d_2 = -\frac{3}{200}$.Now,$\frac{1}{h_{10}} = \frac{1}{h_7} + 3d_2 = \frac{1}{20} + 3\left(-\frac{3}{200}ight) = \frac{10-9}{200} = \frac{1}{200} \Rightarrow h_{10} = 200$.Therefore,$x_5 \cdot h_{10} = 12.8 	imes 200 = 2560$.

If $x_1, x_2, \dots, x_n$ and $\frac{1}{h_1}, \frac{1}{h_2}, \dots, \frac{1}{h_n}$ are two $A.P.s$ such that $x_3 = h_2 = 8$ and $x_8 = h_7 = 20$,then $x_5 \cdot h_{10}$ equals

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