If x1 , x2 , ..., xn and (1/h1) , (1/h2) , ... , (1/hn) are two A.P.s such that x3 = h 2 = 8 and x8 = h7 = 20, then x5 â h10 equals :

Question

If x1 , x2 , ..., xn and (1/h1) , (1/h2) , ... , (1/hn) are two A.P.s such that x3 = h 2 = 8 and x8 = h7 = 20, then x5 â h10 equals : (A) 2560 (B) 2650 (C) 3200 (D) 1600

Tardigrade Admin · Accepted Answer

x1, x2, x3, dots dots.. xn in AP. x3 = 8 x8 = 20 ⇒ x5 = (64/5) h1, h2, h3, dots dots dots hn, in HP h2 = 8, h7 = 20 ⇒ h10 = 200 ⇒ x5 h10 = (64/5)×200 = (12800/5) = 2560

Q. If $x_{1}, x_{2}, ..., x_{n}$ and $\frac{1}{h _{1}}, \frac{1}{h _{2}}, ..., \frac{1}{h _{n}}$ 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 :

2560

2650

3200

1600

$x_{1}, x_{2}, x_{3}, \dots\dots .. x_{n}$ in AP.
$x_{3} = 8 & x_{8} = 20 \Rightarrow x_{5} = \frac{64}{5}$
$h_{1}, h_{2}, h_{3}, \dots\dots\dots h_{n},$ in HP
$h_{2} = 8, h_{7} = 20 \Rightarrow h_{10} = 200$
$\Rightarrow x_{5} h_{10} = \frac{64}{5} \times 200 = \frac{12800}{5} = 2560$

Q. If x1​,x2​,...,xn​ and h1​1​,h2​1​,...,hn​1​ are two A.P.s such that x3​=h2​=8 and x8​=h7​=20, then x5​⋅h10​ equals :