If the sum of first p terms of an ap ap2 + bq find its common difference
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Given: Sp\xa0= ap2\xa0+ bqS1\xa0= a = a(1)2\xa0+ bq = a + bqS2\xa0= a + a2\xa0= a(2)2\xa0+ bq = 4a + bqThen,,. a2\xa0= 4a + bq – a – bq = 3aTherefore, common difference = a2 – a = 3a – a – bq = 2a – bq
Ans. Sp\xa0= ap2+ bqPutting p= 1, we \’ll get some of first one term or first term itselfa1 = a(1)2+ bq\xa0=> a1\xa0= a + bqPutting p=2 we \’ll get sum of first two terms I.e a1+a2S2 = a(2)2 + bq\xa0= 4a+bqa2\xa0= S2-a2=> a2 = 4a + bq – a – bq = 3aCommon difference = a2-a1 = 3a-a-bq = 2a-bq
Given, ap\xa0= ap2\xa0+ bqThen,a = a(1)2\xa0+ bqa2\xa0= a(2)2\xa0+ bq = 4a + bqTherefore,\xa0Common difference = 4a + bq – a – bq = 3a