Question

Suppose the sum of n consecutive integers is x+(x+1) +(x+2) +(x+3)+...+(x+(n-1)) =1000, then which of the following cannot be true about the number of terms n?

• A. The number of terms can be 16
  
• B. The number of terms can be 5
  
• C. The number of terms can be 25
  
• D. The number of terms can be 20

Answer 1

The correct option is D The number of terms can be 20

Solve this question through the options. For n terms being 16 (option 1), we would need an AP with 16 terms and common difference 1, that would add up to 1000. Since, the average value of a term of this AP turns out to be $1000÷16=62.5$, we can create a 16 term AP as 55,56,57....62,63,64...70 that adds up to 1000. Hence, a series of16 consecutive terms is possible. Likewise, a series of 5 terms gives the average as 200 & the 5 terms can be taken as 198,199,200,201,202. It is similarly possible for 25 terms with an average of 40 but is not possible for 20 terms with an average of 50. Hence, option (d) is correct.