[tex]S_n= \frac{n}{2}[(2a_1+(n-1)d][/tex]
n = ? (number of terms)
[tex]a_1 = 10[/tex] (the first term)
[tex]S_n = 2035[/tex] (their sum)
[tex]d = 1[/tex] (common difference of 1 since they are 'consecutive' integers)
[tex]2035= \frac{n}{2}[(2(10)+(n-1)1] \\ \\ 4070= n[20+n-1] \\ \\ 4070=n[19+n] \\ \\ 4070=19n+n^2 \\ \\ n^2+19n-4070= 0 \\ \\ (n+74)(n-55)=0 \\ \\ n=-74\ ;\ \boxed{n=55}[/tex]
