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Delicious77 [7]
3 years ago
13

Prove that the (n+1) term of a G.P of which the first term is a and third term is b,is equal to the (2n+1) term of a G.P of whic

h the first term is a and fifth term is b.
Mathematics
1 answer:
Ahat [919]3 years ago
3 0
Hello,

u_{1} =a\\
 u_{3} =b\\

q= (\dfrac { u_{3} } {u_{1 } }  )^ \frac{1}{2} \\\\\\

=(\dfrac{b}{a}) ^ \frac{1}{2}  \\




 u_{n+1} =a*q^{n}=a* (\dfrac{b}{a}) ^ \dfrac{n}{2} \\


 \\\\\\\\\\\\v_{1} =a\\
 v_{5} =b\\

r= (\dfrac { v_{5} } {v_{1 } }  )^ \frac{1}{4} \\\\\\


 v_{2n+1} =a*r^{2n}\\\\
=a* (\dfrac{b}{a}) ^ \dfrac{2n}{4}\\\\


=a* (\dfrac{b}{a}) ^ \dfrac{n}{2} \\






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Answer:

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Consider "D" the letter to identify distance between A and B

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