**Question 1.**

∴ The reciprocal sequence is not an A.P.

∴ The given sequence is not a H.P.

Solution:

∴ The reciprocal sequence is an A.P.

∴ The given sequence is a H.P.

**Question 2.Find the nth term and hence find the 8th term of the following HPs.**

**Question 3.**

**Question 5.Find G.M. of two positive numbers whose A.M. and H.M. are 75 and 48.Solution:**

**Question 6.**

**Question 7.Insert two numbers between 1 and -27 so that the resulting sequence is a G.P.Solution:**

∴ For resulting sequence to be G.P. we need to insert numbers -3 and 9.

**Question 8.If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by 18/5, find the numbers.Solution:**

Let a and b be the two numbers.

According to the given conditions,

Consider, G = A – 2 = 10 – 2 = 8

ab = 64

a(20 – a) = 64 …..[From (i)]

– 20a + 64 = 0

(a – 4)(a – 16) = 0

∴ a = 4 or a = 16

When a = 4, b = 20 – 4 = 16

When a = 16, b = 20 – 16 = 4

∴ The two numbers are 4 and 16.

**Question 9.**

According to the given conditions,

ab = 36

a(13 – a) = 36 ……[From (i)]

– 13a + 36 = 0

(a – 4)(a – 9) = 0

∴ a = 4 or a = 9

When a = 4, b = 13 – 4 = 9

When a = 9, b = 13 – 9 = 4

∴ The two numbers are 4 and 9.