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समांतर श्रेणी

Question
CBSEHHIMAH10010275

A.P. : 12, 117, 113, ... का कौन-सा पद सबसे पहला ऋणात्मक पद होगा?
[ संकेत: an < 0 के लिए n ज्ञात कीजिए। ]

Solution

A .P. is 121, 117, 113, ... यहाँ, a = 121
d = 117 – 121 = –4
माना nवाँ पद ऋणात्मक पर है अर्थात
straight a subscript straight n space less than space 0
rightwards double arrow space straight a space plus space left parenthesis space straight n space minus space 1 space right parenthesis space straight d space less than space 0
rightwards double arrow space 121 space plus space left parenthesis space straight n space minus space 1 space right parenthesis space left parenthesis space minus space 4 space right parenthesis space less than space 0
rightwards double arrow space 121 space less than space left parenthesis space straight n space minus space 1 space right parenthesis space 4
rightwards double arrow left parenthesis space straight n space minus space 1 space right parenthesis space 4 space greater than space 121
rightwards double arrow space left parenthesis space straight n space minus space 1 space right parenthesis space greater than space 121 over 4
rightwards double arrow space straight n space greater than space 121 over 4 space plus space 1
rightwards double arrow space straight n space greater than space 125 over 4
rightwards double arrow space straight n space greater than space 31 space 1 fourth
अत: दी गई A.P. का 32वाँ पद पहला ऋणात्मक पद है।