Question

find the 10th term of HP 1/2,1/4,1/6........

Answer 1

Answer:

Step-by-step explanation:

For the progression given:

 

1/a= 1/5, a = 5

 

1/(a + d) = 19/4

1/(5 + d) = 19/4

4 = 19(5 + d)

19 = 20 + 4d

-1 = 4d

-1/4 = d

 

The tenth term is 1/(5 + (9)(-1/4))

1/(5 - 9/4)

1/(11/4)

4/11

 

The tenth term is 4/1

Answer 2

Answer:

The 10th term in given series  $\frac{1}{20}$      

Step-by-step explanation:

Given series of HP = $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{6}$ ..  

HP or Harmonic Progression is nothing but reciprocal of the AP or Arithmetic Progression

⇒ given progression can be converted as AP series,  2, 4, 6..  

⇒ first term a = 2, common difference d = 2

⇒ nth term in AP =  a+(n-1)d

⇒  10th term  = 2 + (10-1) 2

                       = 2+ 9(2)

                       = 2 + 18 = 20  

Therefore, 10th term in HP =  $\frac{1}{20}$