Question

Se da sirul de numere naturale:
18,23,28...
1)scrieti al 50-lea termen,al 73-lea si al 200lea
2)calculati suma primilor 100 de termeni!
DAU COROANA

Answer 1

18 , 23 , 28....

T1 = 18 = 5×1+13
T2 = 23 = 5×2+13
T3 = 28 = 5×3+13

Tn = 5×n + 13
T50 = 5×50+13 = 250+13=263
T73 = 5×73+13 = 365+13 = 378
T200 = 5×200+13 = 1013

5×1+13+5×2+13+...+5×100+13 =
= 5×(1+2+...+100) + 13+13+...+13 de 100 de ori
= 5×100×101:2 + 13×100 =
= 5×50×101 + 1300 =
= 250×101+1300 =
= 25250+1300 =
= 26550