Question

Find the sum of the first 100 terms -5, -4, -3, -2, -1, 0, 1, 2 ............. using Gauss method

• A. 4,400
• B. 4,100
• C. 4,200
• D. 4,450

Answer 1

Answer: (D)

4,450

Given that $a=-5,n=100,a_n=?,d=1$
we know that Gauss formula is, $S_n=\frac{n}{2}$ [First term + Last term]
To find nth term,
$a_n=a+(n-1)d$
$a_{100}=-5+(100-1)1$
$=-5+99$
$a_{100}=94$
$S_n=\frac{100}{2}[-5+94]$
$=50\left[89\right]$
$S_{100}=4,450$