Question

If the sum of the first n integers is 15. What is n? (use Gauss method)

• A. 7, 5
• B. 6, -5
• C. 3, -5
• D. 2, 0

Answer 1

Answer: (B)

6, -5

Using Gauss formula,
$S_n=\frac{n}{2}(n+1)$
$15=\frac{n}{2}(n+1)$
$30=n(n+1)$
$30=n^2+n$ ....... (1)
By factorization we can write equation (1) as
$n^2-6n+5n-30=0$
$n(n-6)+5(n-6)=0$
$n=6,-5$
$\therefore$ The n integers will start from -5 to 6.