Question

Find the sum of n terms and also nth term of the series S=(3/5)+(5/15)+(7/45)+(9/135)​+...

Answer 1

Step-by-step explanation:

Calculation of nth term

Let us observe the numerator and the denominators separately.

Sequence of the numerator is 3, 5, 7, 9, .....

Now 5-3 = 7-5=9-7=......2

The sequence has a common difference 2 and hence is an AP with a = 3 and d = 2

So, nth term of numerator is

a + (n-1)d

or 3 + (n-1)2

or 2n + 1

The sequence of deniminator is 5, 15, 45, 135, ....

Now 15/5 = 45/15= 135/45 ....= 3

The sequence has a common ratio 3 and hence it is a GP with a = 5 and r = 3

So, nth term of denominator is

arⁿ⁻¹

or 5.3ⁿ⁻¹

Therefore, nth term of the given series is

tₙ = (2n+1)/5.3ⁿ⁻¹

This type of progression is known as Arithematico-Geometric Progression(AGP)

Answer 2

Answer:

Step-by-step explanation: