Question

in a Hp, a4 =1/9 , a13 = 1/27 , then a7​

Answer 1

The 7 th term of harmonic progression is 1/15.

Given

• Hp
• a4 =1/9
• a13 = 1/27

To find

• a7

Solution

we are provided with a harmonic progression and some terms of the progression and are asked to find the 7th term of harmonic progression.

we know that the recipocal of the harmonic progression forms arithmetic progression,

thus,

1/a4 , 1/a13 etc are terms of AP

let t represent the terms of ap,

t4 = 9

t13 = 27

to find, t7

t4 = 9

9 = p + 3d ... (1)

t13 = 27

27 = p + 12d .....(2)

solving 1 and 2,

d = 2 and p = 3

t7 = 3 + 6d

or, t7 = 3 + 12

or, t7 = 15

Therefore, the 7 th term of harmonic progression is 1/15.

Answer 2

Answer:

Concept:

Basic Mathematics

Step-by-step explanation:

The 7 th term of harmonic progression is 1/15.

Given:

Hp

a4 =1/9

a13 = 1/27

Find:

a7

Solution:

What we have is harmonic progression and we are asked to find the 7th term of harmonic progression.

As we know that the reciprocal of the harmonic progression form arithmetic progression,

Hence,

$1 / a 4,1 / a 13 etc are terms of AP let t represent the terms of ap, t 4=9 \mathrm{t} 13=27 to find, t7 \begin{aligned}&t 4=9 \\&9=p+3 d \ldots(1) \\&t 13=27 \\&27=p+12 d \ldots .(2)\end{aligned} solving 1 and 2 ,$

$d=2 and p=3 t 7=3+6 d or, t 7=3+12 or, \mathbf{t 7}=15 \\So, the 7 th term of harmonic progression is 1 / 15 .$

#SPJ2