Question

Find ratii of a6 and a8 in G.P root 32,root 16,root 8

Answer 1

Answer:

589 - 2=90

Step-by-step explanation:

this ans is helpful

Answer 2

The ratio of $a_6$ and $a_8$ in GP is $1:\frac{1}{2}$

Step-by-step explanation:

Given that the GP is $\sqrt{32},\sqrt{16},\sqrt{8},...$

To find the ratio of $a_6$ and $a_8$ from the given sequence :

• Let $a_1=\sqrt{32}$ ,$a_2=\sqrt{16}$ and $a_3=\sqrt{8}$
• First find the values of $a_6$ and $a_8$
• Since the given sequence is in GP we have that
• The common ratio $r=\frac{a_2}{a_1}$
• Substitute the values we get
• $r=\frac{\sqrt{16}}{\sqrt{32}}$

• $=\frac{\sqrt{16}}{\sqrt{16\times 2}}$
• $=\frac{\sqrt{16}}{\sqrt{16}\times \sqrt{2}}$

Therefore $r=\frac{1}{\sqrt{2}}$

• The common ratio $r=\frac{a_3}{a_2}$

• Substitute the values we get
• $r=\frac{\sqrt{8}}{\sqrt{16}}$

• $=\frac{\sqrt{8}}{\sqrt{8\times 2}}$
• $=\frac{\sqrt{8}}{\sqrt{8}\times \sqrt{2}}$

Therefore $r=\frac{1}{\sqrt{2}}$

Therefore the common ratio is $r=\frac{1}{\sqrt{2}}$

Now to find $a_6$

The general formula for GP is $a_n=ar^{n-1}$

• Substitute n=6 , $a_1=\sqrt{32}$ and $r=\frac{1}{\sqrt{2}}$ in the formula we get
• $a_6=\sqrt{32}(\frac{1}{\sqrt{2}})^{6-1}$
• $=\sqrt{32}(\frac{1}{\sqrt{2}})^{5}$
• $=\sqrt{32}(\frac{1}{(\sqrt{2})^5})$
• $=\sqrt{32}(\frac{1}{\sqrt{32}})$
• $=1$

Therefore $a_6=1$

Now finding $a_8$

• Substitute n=8 , $a_1=\sqrt{32}$ and $r=\frac{1}{\sqrt{2}}$ in the formula we get
• $a_6=\sqrt{32}(\frac{1}{\sqrt{2}})^{8-1}$
• $=\sqrt{32}(\frac{1}{\sqrt{2}})^{7}$
• $=\sqrt{32}(\frac{1}{(\sqrt{2})^7})$
• $=\sqrt{32}(\frac{1}{\sqrt{32\times 4}})$
• $=\frac{1}{\sqrt{4}}$

Therefore $a_8=\frac{1}{2}$

The ratio of $a_6$ and $a_8$  in GP is

$1:\frac{1}{2}$