Question

show that the progression 2,2√2,4,4√2......is a G.P. (1)FIND it's first term, (2)common ratio, (3)nth term (4)11th term​

Answer 1

Step-by-step explanation:

1. Given series

  $\mathbf{2,2\sqrt{2},4,4\sqrt{2}...}$

2.Here we see that second term is obtain by multiply by $\mathbf{\sqrt{2}}$ to first term.

  Similarly

  Third term is obtain by multiply by $\mathbf{\sqrt{2}}$ to second term.

  Fourth term is obtain by multiply by $\mathbf{\sqrt{2}}$ to third term.

  So this is in Geometric progression series.

  Above can also prove by another method, find ratio of two consecutive term

   $\mathbf{\frac{2\sqrt{2}}{2}=\frac{4}{2\sqrt{2}}=\frac{4\sqrt{2}}{4}=\sqrt{2}}$  means ratio is same. so it is in G.P series.  

3. Here

  First term (a)= 2

  Common ration (r)$\mathbf{=\frac{2\sqrt{2}}{2}=\sqrt{2}}$

4. $\mathbf{N^{th} \ term \ (T_{N})=ar^{n-1}}$

  After putting value of a and r in above equation

  $\mathbf{(T_{N})=2\times (\sqrt{2})^{n-1}=2\times 2^{\frac{n-1}{2}}=2^{\left ( 1+\frac{n-1}{2} \right )}}$

  After solving

  $\mathbf{N^{th} \ term \ (T_{N})=2^{\frac{n+1}{2}}}$          

5. Eleventh term can be obtain by putting the value of n is 11 in above

   equation

  $\mathbf{11^{th} \ term \ (T_{11})=2^{\frac{11+1}{2}}=2^{\frac{12}{2}}=2^{6}=64}$

Answer 2

Answer:

the answer is in the attachment

Step-by-step explanation:

hope that it might have helped u

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