In an arithmetic sequence of common difference 3,out of first 25terms sum of first 13 terms is equal to sum of next 12 terms what is the difference between first term and 14 th term? What is the difference between 12th and 25th term?

Asked by vinodar2003 | 25th Aug, 2019, 02:48: PM

Expert Answer:

S u m space o f space 1 s t space 13 space t e r m s space i s space S subscript 13 equals 13 over 2 open parentheses 2 a plus 12 d close parentheses equals 13 over 2 open parentheses 2 a plus 12 cross times 3 close parentheses equals 13 over 2 open parentheses 2 a plus 36 close parentheses
F o r space t h e space s u m space o f space n e x t space 12 space t e r m s comma space f i r s t space t e r m space equals space t subscript 14 equals a plus 13 d equals a plus 39
S u m space o f space n e x t space 12 space t e r m s space equals space 12 over 2 open parentheses 2 open parentheses a plus 13 d close parentheses plus 11 d close parentheses equals 6 open parentheses 2 a plus 2 cross times 39 plus 11 cross times 3 close parentheses equals 6 open parentheses 2 a plus 111 close parentheses
G i v e n colon
S u m space o f space f i r s t space 13 space t e r m s equals S u m space o f space n e x t space 12 space t e r m s
rightwards double arrow 13 over 2 open parentheses 2 a plus 36 close parentheses equals 12 over 2 open parentheses 2 a plus 111 close parentheses
rightwards double arrow 26 a plus 13 cross times 36 equals 24 a plus 12 cross times 111
rightwards double arrow a equals 432
open vertical bar t subscript 14 minus t subscript 1 close vertical bar equals open vertical bar a plus 39 minus a close vertical bar equals 39
open vertical bar t subscript 12 minus t subscript 25 close vertical bar equals open vertical bar a plus 33 minus left parenthesis a plus 72 right parenthesis close vertical bar equals 39

Answered by Renu Varma | 26th Aug, 2019, 10:47: AM

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