Show that the following sequences are H.P. Also, find 10th term in each case.
i) 1/2, 1/5, 1/8, 1/11,...
ii) 2/9, 1/7, 2/19, 1/12, ...
Answers
Answer:
Step-by-step explanation:
Concept:
A sequence is said to be in H.P if reciprocal of their terms are in A.P.
The nth term of AP is a +(n-1)d
i) 1/2, 1/5, 1/8, 1/11,......
Its reciprocal is
2, 5, 8, 11........
Clearly it is an A.P with common difference 3
Hence 1/2, 1/5, 1/8, 1/11,...... is in H.P
11 th term of 2, 5, 8, 11........is
a + 10d
= 2+10(3)
= 32
Hence, the 11th term of the H.P
1/2, 1/5, 1/8, 1/11,...... is 1/32
ii) 2/9, 1/7, 2/19, 1/12, ...
Its reciprocal is
9/2, 7, 19/2, 12.....
Clearly it is an A.P with common difference 2.5
Hence 2/9, 1/7, 2/19, 1/12, ...is in H.P
11 th term of 9/2, 7, 19/2, 12..... is
a + 10d
= 4.5 + 10(2.5)
= 4.5 + 25
= 29.5
= 59/2
Hence the 11th term of the H.P
2/9, 1/7, 2/19, 1/12, .....is 2/59
Step-by-step explanation:
so ans of 1). 1/29. &. 2). 1/27. i hope it is useful. please mark as brainlist
