Question

Determine the 4th and 8th term of the Harmonic progression 6, 4, 3.....

Answer 1

Explanation:

Given:

H.P = 6, 4, 3

Now, let us take the arithmetic progression from the given H.P

A.P = ⅙, ¼, ⅓, ….

Here, T2 -T1 = T3 -T2 = 1/12 = d

So, in order to find the 4th term of an A. P, use the formula,

The nth term of an A.P = a+(n-1)d

Here, a = ⅙, d= 1/12

Now, we have to find the 4th term,

So, take n=4

Now put the values in the formula, we have

4th term of an A.P = (⅙) +(4-1)(1/12)

= (⅙)+(3/12)

= (⅙)+ (¼)

= 5/12

Similarly, for 8th term of an A.P,

8th term of an A.P = (⅙) +(8-1)(1/12)

= (⅙)+(7/12)

= 9/12

Since H.P is the reciprocal of an A.P, we can write the values as:

4th term of an H.P = 1/4th term of an A.P = 12/5

8th term of an H.P = 1/8th term of an A.P = 12/9 = 4/3