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Find the sum of all two digit natural numbers when divide by three yield 1 as reminder |
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Answer» is 1605Step-by-step explanation:The 2-digit number which when divided by 3 GIVES remainder 1 are: 10, 13, 16, ...97Here a = 10, d = 13 - 10 = 3tn = 97nth term of an AP is TN = a + (n – 1)d97 = 10 + (n – 1)3⇒ 97 = 10 + 3n – 3⇒ 97 = 7 + 3n⇒ 3n = 97 – 7 = 90∴ n = 90/3 = 30Recall sum of n terms of AP, = 15[20 + 87] = 15 × 107 = 1605Hence sum of 2-digit numbers which when divided by 3 yield 1 as remainder is 1605. |
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