**Q.1.** If the sum of reciprocals of first 11 terms of an HP series is 110, find the 6^{th} term of HP.

- 1/5
- 1/10
- 2/7
- 1/20

**Answer: Option B**

**Explanation:** Now from the above HP formulae, it is clear the reciprocals of first 11 terms will make an AP. The sum of first 11 terms of an AP = [2a + (11 – 1) d] 11/2 = 110

⇒ 2a + 10d = 20 ⇒ a + 5d = 10

Now there are 2 variables, but a + 5d = T_{6} in an AP series. And reciprocal of 6^{th} term of AP series will give the 6^{th} term of corresponding HP series. So, the 6^{th} term of HP series is 1/10

**Q.2.** Find the 4th and 8th term of the series 6, 4, 3, …

- 12/5 and 4/3
- 7/10 and 5/7
- 1/7 and 3/4
- 20/11 and 9/8

**Answer: Option A**

**Explanation:** Consider 1/6, /14, 1/3, ...

Here T_{2} – T_{1} = T_{3} – T_{2} = 1/12

Therefore 1/6, 1/4, 1/3 is in A.P.

4th term of this Arithmetic Progression = 1/6 + 3 × 1/12 = 1/6 + 1/4 = 5/12,

Eighth term = 1/6 + 7 × 1/12 = 9/12.

Hence the 8th term of the H.P. = 12/9 = 4/3 and the 4th term = 12/5.

**Q.3.** The 2nd term of an HP is 40/9 and the 5th term is 20/3. Find the maximum possible number of terms in H.P.

- 11
- 10
- 9
- 12

**Answer: Option B**

**Explanation :** If a, a + d, a + 2d, a + 3d, ……. are in A.P. then

are in H.P.

Now

and

Solving these two equations we get

and

Now

Hence the maximum terms that this H.P. can take is 10.

**Q.4.** If the first two terms of a harmonic progression are 1/16 and 1/13, find the maximum partial sum?

- 1.63
- 1.13
- 1.89
- 2.2

Answer: Option A

**Explanation :** The terms of the HP are

So the maximum partial sum is

**Q.5.** The second term of an H.P. is

and the fifth term is

. Find the sum of its 6

^{th} and the 7

^{th} term.

- 177/1547
- 145/1457
- 513/3233
- 117/3123

**Answer: Option C**

**Explanation: ** If a, a + d, a + 2d, a + 3d, ……. are in A.P. then

are in H.P.

Now

and

Solving these two equations, we get

and

Now

And

So the sum of the 6

^{th} and the 7

^{th} term of H.P. is

**Q.6.** If the sixth term of an H.P. is 10 and the 11th term is 18 Find the 16th term.

- 30
- 75
- 90
- 80

**Answer: Option C**
**Explanation:** Here

And

Solving these two equations, we get

and

We have

Hence the 16

^{th} term is 90.