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ICSE Class 10 Answered

What is the commen difference if the sum of first 10 terms of an arithmatic sequance is 320and the sum of first to 15 terms is 705
Asked by risha123rish | 05 Mar, 2020, 11:20: AM
answered-by-expert Expert Answer
Here, S10 = 320 and S15 = 705
We know that,
begin mathsize 16px style straight S subscript straight n space equals space straight n over 2 open square brackets 2 straight a plus open parentheses straight n minus 1 close parentheses straight d close square brackets rightwards double arrow straight S subscript 10 space equals space 10 over 2 open square brackets 2 straight a plus open parentheses 10 minus 1 close parentheses straight d close square brackets rightwards double arrow 320 space equals 5 open parentheses 2 straight a space plus space 9 straight d close parentheses rightwards double arrow 2 straight a space plus space 9 straight d equals space 64 space space space space space... space left parenthesis straight i right parenthesis Also comma space straight S subscript 15 space equals space 15 over 2 open square brackets 2 straight a plus open parentheses 15 minus 1 close parentheses straight d close square brackets rightwards double arrow 705 space equals 15 over 2 open parentheses 2 straight a space plus space 14 straight d close parentheses rightwards double arrow straight a space plus space 7 straight d equals space 47 space space rightwards double arrow straight a space equals space 47 space minus space 7 straight d Substitute space the space value space of space straight a space in space the space equation space left parenthesis straight i right parenthesis comma space we space get 2 straight a space plus space 9 straight d equals space 64 rightwards double arrow 2 open parentheses 47 space minus space 7 straight d close parentheses space plus space 9 straight d space equals space 64 rightwards double arrow straight d space equals space 6 end style
Answered by Yasmeen Khan | 05 Mar, 2020, 12:56: PM

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