Profile Photo

Narasimha

Jul 14 2013

Kishore answered 5 month(s) ,28 day(s) ago

Find the sum of all 2-digit natural numbers

find the sum of all 2-digit natural numbers which when divided by 3 yield 1 as remainder.

Answer List
Kishore, Student
178 days, 16 hours ago
Profile Photo
The 2-digit number which when divided by 3 gives remainder 1 are: 10, 13, 16, ...97
Here a = 10, d = 13 - 10 = 3
tn = 97
nth term of an AP is tn = a + (n – 1)d
97 = 10 + (n – 1)3
⇒ 97 = 10 + 3n – 3
⇒ 97 = 7 + 3n
⇒ 3n = 97 – 7 = 90
∴ n = 90/3 = 30
Recall sum of n terms of AP,

= 15[20 + 87] = 15 × 107 = 1605
Hence sum of 2-digit numbers which when divided by 3 yield 1 as remainder is 1605.
Profile Photo

,

Have Study Related Doubts?

  • Ask and clear all your doubts
  • Get help from Subject Matter Experts
About Us|Contact Us|Terms of Use|Privacy Statement|Disclaimer|Copyright|Sitemap|Testimonials|Product Tour
© 2013 Next Education. All rights reserved.