Question

Det x apartine lui R astfel incat 1+4+7+...+x=651

Answer 1

1, 4, 7, . . . x sunt termenii consecutivi ai unei progresii aritmetice cu a1=1 si r=3     
Sn=[2a1 + (n-1)×r]×n/2   
651 = [2×1 + (n-1)×r]×n/2
2×651 = [2 + (n-1)×3]×n
1302 = (2 + 3n - 3)×n
1302 = (3n - 1)×n
3n² - n - 1302 = 0
Δ = b² - 4ac = 1² - 4×3×(-1302) = 1 + 15624 = 15625
n1 = (-b + √Δ)/2a = (1 + 125)/6 = 126/6 = 21 (solutie)
n2 = (-b - √Δ)/2a = (1 - 125)/6 = 124/6 nu convine
x = a21 = a1 + (n-1)×r = 1 + 20×3 = 1 + 60 = 61