CBSE Class 10 Answered
If the pth term of an AP is 1/q and qth term 1/P. Prove that the sum of the first pqth term is 1/2 (pq + 1).
Asked by latayadav23 | 17 Oct, 2023, 20:39: PM
Let a be the first term and d be the common difference of Arithmetic progression
pth term :- a + (p-1)d = (1/q) ........................ (1)
qth term :- a + ( q-1) d = ( 1/p ) .................... (2)
By subtracting eqn.(2) from eqn.(1) , we get
![begin mathsize 14px style left parenthesis space p space minus space q space right parenthesis space d space equals space 1 over q minus fraction numerator 1 over denominator p space end fraction equals space fraction numerator p minus q over denominator p q end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/4da5265bcb6255a2967e8ad85dd63c4d.png)
![begin mathsize 14px style d space equals space fraction numerator 1 over denominator p space q end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/88d7ec91a5007da390216e6c29a5224c.png)
By substituting d in eqn.(1) , we get
![begin mathsize 14px style a space plus space fraction numerator left parenthesis p minus 1 right parenthesis over denominator p space q end fraction space equals space 1 over q end style](https://images.topperlearning.com/topper/tinymce/cache/54bdf34008da3becc8de49a906145bbd.png)
from above expression , we get a = 1 / (pq)
Hence sum S of (pq) terms is
![begin mathsize 14px style S space equals space fraction numerator p q over denominator 2 end fraction open square brackets fraction numerator 1 over denominator p q end fraction plus space left parenthesis p q minus 1 right parenthesis fraction numerator 1 over denominator p q end fraction close square brackets space equals space 1 half left parenthesis p q plus 1 right parenthesis end style](https://images.topperlearning.com/topper/tinymce/cache/930d772819e7f7e4d254e00136b21c88.png)
Answered by Thiyagarajan K | 17 Oct, 2023, 23:03: PM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by lp9128437598 | 10 Jun, 2024, 10:34: AM
CBSE 10 - Maths
Asked by deepikaselvam2009 | 20 Feb, 2024, 20:57: PM
CBSE 10 - Maths
Asked by keshavsinghalhapur | 16 Jan, 2024, 20:46: PM
CBSE 10 - Maths
Asked by keshavsinghalhapur | 15 Jan, 2024, 10:56: AM
CBSE 10 - Maths
Asked by skandachiranjeevin | 06 Dec, 2023, 19:08: PM
CBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 23:24: PM
CBSE 10 - Maths
Asked by latayadav23 | 17 Oct, 2023, 20:39: PM
CBSE 10 - Maths
Asked by ananya_monica | 28 Sep, 2023, 19:07: PM
CBSE 10 - Maths
Asked by simmysingh1aug | 20 Sep, 2023, 22:20: PM
CBSE 10 - Maths
Asked by bkhaiwangkonyak | 07 Mar, 2023, 16:35: PM