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NDA 2019 Maths · Mathematics · Sequences and Series · medium

The sum of all natural numbers between 10 and 100 that are multiples of 4 is

Single correct option

The sum of all natural numbers between 1010 and 100100 that are multiples of 44 is
  1. A. 13001300
  2. B. 12241224
  3. C. 13121312
  4. D. 12881288
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Answer: (D) 12881288

The multiples are 12,16,…,10012,16,\ldots,100, an AP with a=12a=12, l=100l=100, d=4d=4. The number of terms is 100−124+1=23\dfrac{100-12}{4}+1=23. The sum is 232(12+100)=1288\dfrac{23}{2}(12+100)=1288. The value 13121312 includes 88 and the value 13001300 is the result of counting 2222 terms; the count of terms is the usual place for error.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake