Question

The nth term of H.P, whose first two terms are 6 and 3 respectively is​

Answer 1

Step-by-step explanation:

a n =6+(n-1) *(-3)

a n = 6-3n+3

a n = 3 -3n

Hence n th term of AP is 3-3n

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Answer 2

The nth term of the harmonic progression would be, 6/n

Given

• first two terms are 6 and 3
• H.P

To find

• The nth term of H.P

Solution

we are provided with harmonic mean and it first two terms and are asked to find the nth the term of the same harmonic progression.

the reciprocal of harmonic progression terms gives arithmetic progression,

1/6 , 1/3 are first two terms of arithmetic progression,

therefore the common difference of the arithmetic progression would be,

d = 1/3 - 1/6

or, d = (2-1)/6

or, d = 1/6

now the n th term of the arithmetic progression would be,

an = a + (n-1)d

or, an = 1/6 + (n-1)1/6

or, an = 1/6{ 1 +n -1}

or, an = n/6

Therefore, the nth term of the harmonic progression would be, 6/n

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