Question

find the nth term of H.P 1/4,1/6,1/8,1/10,....
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Answer 1

Answer:

The nth term of HP is  1/(2+2n)

Step-by-step explanation:

Given that 1/4 , 1/6 , 1/8 , 1/10 is in HP

We know that if a,b,c,d is in AP then 1/a , 1/b , 1/c , 1/d is in HP

Similarly, here, 4, 6, 8, 10 will be in AP

Therefore for this AP,

a = 4 , d = 2 ,

aₙ = 4 + (n - 1) 2

aₙ = 4 + 2n -2

aₙ = 2 + 2n

As every term of AP is reciprocal of the same term of HP

Then, nth term of HP is 1/aₙ = 1/(2+2n)

Therefore, the nth term of HP is  1/(2+2n)