The sum of the numbers between 100 and 1000 which are divisible by 14 is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 35392
The numbers divisible by 14 form an arithmetic progression with common difference 14. Find its first and last terms between 100 and 1000, count the terms, and use \(S=\frac{n}{2}(a+l)\).
First term: \(14\times8=112\) (\(14\times7=98\) is below 100)
Last term: \(14\times71=994\) (\(14\times72=1008\) is above 1000)
Number of terms \(=71-8+1=64\)
Sum \(\displaystyle=\frac{64}{2}(112+994)=32\times1106=35392\)