Question

In a GP the product of rth term from beginning and rth term from the end is equal to ptoduct of first term and last term. Prove it.

Answer 1

Answer:

Step-by-step explanation:

1. Well in Geometric Progression, next term is obtained by multiplying fixed no. to previous term. So, all terms systematically varies.
2. To explain product of rth term from beginning and rth term from the end is equal to product of first term and last term, let's have a example of GP             2, 4, 8, 16, 32, 64
3. The product of rth term from beginning and ending, 4 × 32 =128
4. The product of first and end term, 2 × 64 = 128.

I hope it will help you.

Answer 2

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 term from the end = n - r + 1 th term

rth term from the end $= ax^{(n-r+1-1)} = ax^{(n-r)}$

Product of rth term from beginning and rth term from the end

= $a * x^{(r-1)} * a * x^{(n-r)} = a^2 * x^{(r-1 + n-r)} = a^2 * x^{(n-1)}$

= 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