Question

16.) In a finite GP, prove that the product of the terms equidistant from the
beginning and end is the product of first and last terms.​

Answer 1

Answer:

Let a be the first term, r be the common ratio and l be the last term of a GP containing n terms.

Then,

(pth term from the beginning)×(pth term from the end)

=(pth term from the beginning)×{(n−p+1)the term from teh beginning}

=T

p

×T

(n−p+1)

=ar

p−1

×ar

(n−p+1)−1

=ar

(p−1)

×ar

(n−p)

=a×(ar

n−1

)=(T

1

×T

n

)=(first term × last term).