CBSE Class 11-science Answered
if the pth term of a hp is q and the qth term is p,prove that its (p+q)th term is pq/p+q
Asked by | 15 Aug, 2012, 07:05: PM
Expert Answer
Given,
Tp = q............ in HP
Tq = p............ in HP
Therefore, In AP
Tp = 1 / q
Tq = 1 / p
d = Tp - Tq / p - q
= (1 / q) - (1 / p) / p - q
= (p - q / pq) / p - q
Therefore,
d = 1 / pq
Again,
Let Tp+q = X
d = Tp - Tp+q / p - ( p + q)
1 / pq = 1 / q - X / q
X = 1 / p + 1 / q
X = p + q / pq.............. in AP
Therefore, in HP, Tp+q = pq / p+q
Tq = p............ in HP
Therefore, In AP
Tp = 1 / q
Tq = 1 / p
d = Tp - Tq / p - q
= (1 / q) - (1 / p) / p - q
= (p - q / pq) / p - q
Therefore,
d = 1 / pq
Again,
Let Tp+q = X
d = Tp - Tp+q / p - ( p + q)
1 / pq = 1 / q - X / q
X = 1 / p + 1 / q
X = p + q / pq.............. in AP
Therefore, in HP, Tp+q = pq / p+q
Answered by | 15 Aug, 2012, 10:28: PM
Concept Videos
-
Introduce the concept of sequences and series, their types and specific typ... -
This video covers examples on condition for a sequence to be an arithmetic ... -
This video explains the geometric Mean of two numbers and inserting numbers... -
This video covers examples related to Summation of a series containing squa... -
This video explains the arithmetic mean of two numbers, inserting n numbers...
CBSE 11-science - Maths
Asked by sakshirana374 | 24 Jul, 2022, 05:39: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by sanjuktamukherjee165 | 24 Oct, 2021, 11:04: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by rahulksinha200 | 16 Oct, 2021, 02:08: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by Vibhorjarora798 | 21 Aug, 2021, 05:43: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by shivangkarol | 16 Jun, 2021, 01:18: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by minkukumarprasad94839483 | 05 Feb, 2021, 08:49: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by hirugadeshravani | 26 Dec, 2020, 07:37: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by gurijoga368 | 28 Sep, 2020, 12:20: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by mahavenkat152004 | 25 Jul, 2020, 07:49: PM
ANSWERED BY EXPERT