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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, 07:13: PM
answered-by-expert Expert Answer
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
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
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
Answered by Thiyagarajan K | 15 Dec, 2018, 10:29: PM
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