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  • Find the 20 th and n th terms of the G.P. 5 by 2 , 5 by 4 , 5 by 8

1.  Find the 20 ^{th} and n ^{th} terms of the G.P. \frac{5}{2},\frac{5}{4},\frac{5}{8},....
 

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best_answer

G.P : 

            \frac{5}{2},\frac{5}{4},\frac{5}{8},....

first term = a

   a=\frac{5}{2}

common ratio =r

r=\frac{\frac{5}{4}}{\frac{5}{2}}=\frac{1}{2}

a_n=a.r^{n-1}

a_2_0=\frac{5}{2}.(\frac{1}{2})^{20-1}

a_2_0=\frac{5}{2}.(\frac{1}{2^{19}})

a_2_0=\frac{5}{2^{20}}

a_n=a.r^{n-1}

a_n=\frac{5}{2}.\left ( \frac{1}{2} \right )^{n-1}

a_n=\frac{5}{2}. \frac{1}{2^{n-1}}

a_n=\frac{5}{2^n}   the nth term of G.P

 

Posted by

seema garhwal

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