Question

5th term if GP is 1/162 and 76 th term is 1/486 then find GP

Answer 1

Answer:

which std question is this?

Answer 2

First term is $\mathbf{\frac{1}{2}}$ and common ratio is $\mathbf{\frac{1}{3}}$

Step-by-step explanation:

1. Let

   First term in G.P  =a

   Common ratio = r

2. Given that

   Fifth term $\mathbf{(T_{5})=ar^{5-1}=\frac{1}{162}}$

   Means

   $\mathbf{T_{5}=ar^{4}=\frac{1}{162}}$        ...1)

3. In question mention that 76 term but it should be Six term

   $\mathbf{T_{6}=ar^{6-1}=\frac{1}{486}}$

   Means

   $\mathbf{T_{6}=ar^{5}=\frac{1}{486}}$       ...2)

4. Divide equation 2) by equation 1), we get

   $\mathbf{\frac{T_{6}}{T_{5}}=\frac{ar^{5}}{ar^{4}}=\frac{\frac{1}{486}}{\frac{1}{162}}}$

   So

   $\mathbf{r=\frac{162}{486}}$

   $\mathbf{r=\frac{1}{3}}$        ...3)

5. From equation 1) and equation 3)

   $\mathbf{ar^{4}=\frac{1}{162}}$

   $\mathbf{a\left ( \frac{1}{3} \right )^{4}=\frac{1}{162}}$

   $\mathbf{\frac{a}{81}=\frac{1}{162}}$

  So

   $\mathbf{a=\frac{1}{2}}$

6. Now

   First term = $\mathbf{T_{1}=a=\frac{1}{2}}$

   Second term = $\mathbf{T_{2}=ar=\frac{1}{6}}$

   Third term = $\mathbf{T_{3}=ar^{2}=\frac{1}{18}}$

   Fourth term = $\mathbf{T_{4}=ar^{3}=\frac{1}{54}}$

   Fifth term =$\mathbf{T_{5}=ar^{4}=\frac{1}{162}}$

   Sixth term = $\mathbf{T_{6}=ar^{5}=\frac{1}{486}}$

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