Question

calculati suma S=7+17+27+....+1997+2007

Answer 1

S = 7    +   17+    27+....+1987+1997+2007
S =2007+1997+1987+....+   27+     17+    7
_________________________________________
2S = 2014+2014+2014+...+2014+2014+2014

Stabilim cate numere se afla  in  primul sir de numere

7+10*0, 7+10*1, 7+10*2,............7+10*200
Avem  201  numere
2 S =  2014 * 201
2 S =   404814
 S = 404814 / 2
 S = 202407                                

Answer 2

$\displaystyle 7+17+27+...+1997+2007 \\ 2007=7+(n-1) \times 10 \\ 2007=7+10n-10 \\ 10n=2007-7+10 \\ 10n=2010 \\ n=2010:10 \\ n=201 \\ S_{201}= \frac{14+200 \times 10}{2} \times 201 \\ \\ S_{201}= \frac{14+2000}{2} \times 201 \\ \\ S_{201}= \frac{2014}{2} \times 201 \\ \\ S_{201}=1007 \times 201 \\ S_{201}=202407$