Chapter 2 Sequences and Series Ex 2.4
Chapter 2 Sequences and Series Ex 2.4
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.
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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.