Find the sum of all two-digit numbers divisible by 2 or 3. Share with your friends Share 7 Manbar Singh answered this The list of 2 digit numbers that are divisible by 2 is :10, 12, 14, ........98.The above list is an AP with first term, a = 10 and common difference, d = 2Now, an = 98⇒a + n-1d = 98⇒10+n-12 = 98⇒2n-1 = 88⇒n-1 = 44⇒n = 45Now, sum of first n terms of an AP is Sn = n22a+n-1d⇒S45 = 4522×10+45-12 = 45220+88 = 2430The list of 2 digit numbers that are divisible by 3 is :12, 15, 18, 21, ........99.The above list is an AP with first term, a = 12 and common difference, d = 3Now, an = 99⇒a+n-1d = 99⇒12+n-13 = 99⇒3n-1 = 87⇒n-1 = 29⇒n = 30S30 = 3022×12+30-13 = 1524+87 = 1665The list of 2 digit numbers that are divisible by 6 is :12, 18, 24, .........96.The above list is an AP with first term, a = 12 and common difference, d = 6.Now, an = 96⇒a+n-1d = 96⇒12+n-16 = 96⇒6n-1 = 84⇒n-1 = 14⇒n = 15Now, S15 = 1522×12+15-16 = 15224+84 = 810Now, required sum of 2 digit numbers that is either divisible by 2 or 3 = 2430+1665-810 = 3285 12 View Full Answer