Question

Se considera sirul de nr. 6, 13, 20, 27,34,........ . Calculati suma primilor 2015 termeni ai sirului.

Answer 1

6, 13, 20, 27, 34, ...

Termen 1 = 6 = 7 × 1 - 1
Termen 2 = 13 = 7 × 2 - 1
Termen 3 = 20 = 7 × 3 - 1
Termen 4 = 27 = 7 × 4 - 1
Termen 5 = 34 = 7×5 - 1
............
Termen 2015 = 7×2015 - 1 = 14 104

S = 6 + 13 + 20 + 27 + 34 +...+ 14 104

S = 2015 × (6+14104) : 2

S = 2015 × 14110 : 2

S = 2015 × 7055

S = 14 215 825

Answer 2

6, 13, 20, 27, 34.

Creste cu 7, vom avea ceva ori 7 - ceva. Incercam sa ne dam seama.

(1×7-1), (2×7-1), (3×7-1), (4×7-1), (5×7-1)

S = (1×7-1) + (2×7-1) + (3×7-1) + (4×7-1) + (5×7-1)+...+(2015×7-1)

S= 7×(1+2+3+4+5+...+2015) - 1×2015
S = 7×(2015×(2015+1) : 2) - 2015
S = 7×2015×2016:2 - 2015
S = 7×2015×1008 - 2015
S = 2015×(7×1008-1)
S = 2015×7055
S = 14.215.825