CBSE Class 10 Answered
Page 255
Question 23
The sums of n terms of three arithmetic progressions are S1, S2, and S3.The first term of each is unity and the common differences are 1,2 and 3 respectively. Prove that S1+S3=2S2
Asked by miniprasad | 15 Dec, 2018, 19:13: PM
S1 = (1/2) n×(n+1) ;
S2 = ![begin mathsize 12px style n over 2 open square brackets 2 plus left parenthesis n minus 1 right parenthesis cross times 2 close square brackets space equals space n squared end style](https://images.topperlearning.com/topper/tinymce/cache/2479abaa198b596c9ef969244a0fbdcb.png)
![begin mathsize 12px style n over 2 open square brackets 2 plus left parenthesis n minus 1 right parenthesis cross times 2 close square brackets space equals space n squared end style](https://images.topperlearning.com/topper/tinymce/cache/2479abaa198b596c9ef969244a0fbdcb.png)
S3 = ![begin mathsize 12px style n over 2 open square brackets 2 space plus space open parentheses n minus 1 close parentheses cross times 3 close square brackets space equals space fraction numerator n left parenthesis 3 n minus 1 right parenthesis over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/f97f63830f3bc3502c2e4feb6bb85dd7.png)
![begin mathsize 12px style n over 2 open square brackets 2 space plus space open parentheses n minus 1 close parentheses cross times 3 close square brackets space equals space fraction numerator n left parenthesis 3 n minus 1 right parenthesis over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/f97f63830f3bc3502c2e4feb6bb85dd7.png)
S1+S3 = ![begin mathsize 12px style n over 2 open square brackets n plus 1 plus 3 n minus 1 close square brackets space equals space 2 n squared space equals space 2 S subscript 2 end style](https://images.topperlearning.com/topper/tinymce/cache/65ade0537bb3af99cbc0f3ce5f243e57.png)
![begin mathsize 12px style n over 2 open square brackets n plus 1 plus 3 n minus 1 close square brackets space equals space 2 n squared space equals space 2 S subscript 2 end style](https://images.topperlearning.com/topper/tinymce/cache/65ade0537bb3af99cbc0f3ce5f243e57.png)
Answered by Thiyagarajan K | 15 Dec, 2018, 22:29: PM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by dheerrana109 | 22 Jul, 2024, 10:26: AM
CBSE 10 - Maths
Asked by vishwanathhikkalagutti | 17 Jul, 2024, 07:25: AM
CBSE 10 - Maths
Asked by avadheshkumar94 | 13 Jul, 2024, 20:18: PM
CBSE 10 - Maths
Asked by 3ra2231 | 11 Jul, 2024, 20:55: PM
CBSE 10 - Maths
Asked by avadheshkumar94 | 10 Jul, 2024, 10:14: AM
CBSE 10 - Maths
Asked by syashkurun | 08 Jul, 2024, 19:14: PM
CBSE 10 - Maths
Asked by francissaka528 | 08 Jul, 2024, 06:15: AM
CBSE 10 - Maths
Asked by radhe9868017031 | 05 Jul, 2024, 14:10: PM
CBSE 10 - Maths
Asked by naidulokesh892 | 04 Jul, 2024, 20:42: PM