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.