In a finite GP, prove that the product of the terms equidistant from the beginning and end is the product of first and last term
Answers
Step-by-step explanation:
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Answer:
Answer:
Product of rth term from beginning and rth term from the end = product of first term and last term
Step-by-step explanation:
Let say there are n terms in GP
first term = a
Common Ratio = x
nth Term = a * xⁿ⁻¹
product of first term and last term = a * a * xⁿ⁻¹ = a²xⁿ⁻¹
Term rth = a * x^{(r-1)}rth=a∗x
(r−1)
rth term from the end = n - r + 1 th term
rth term from the end = ax^{(n-r+1-1)} = ax^{(n-r)}=ax
(n−r+1−1)
=ax
(n−r)
Product of rth term from beginning and rth term from the end
= a * x^{(r-1)} * a * x^{(n-r)} = a^2 * x^{(r-1 + n-r)} = a^2 * x^{(n-1)}a∗x
(r−1)
∗a∗x
(n−r)
=a
2
∗x
(r−1+n−r)
=a
2
∗x
(n−1)
= a²xⁿ⁻¹
= product of first term and last term
Product of rth term from beginning and rth term from the end = product of first term and last term