Question

Calculeaza sumele: a)s=4+7+10+...+91 b)s=6+11+16+21+...+101

Answer 1

a)
S =4+7+10+...+91
S = 3×1+1 + 3×2+1 + 3×3+1 +...+ 3×30+1
S = 3×(1+2+3+...+30) + 1+1+1+..+1 de 30 ori
S = 3 × 30 × 31 : 2 + 1 × 30
S = 3 × 15 × 31 + 30
S = 1 395 + 30
S = 1 425

b)
S = 6+11+16+21+...+101
S = 5×1+1 + 5×2+1 +5×3+1 + 5×4+1 +...+ 5×20+1
S = 5×(1+2+3+4 +...+20) + 1+1+1+...+1 de 20 ori
S = 5 × 20 × 21 : 2 + 1 × 20
S = 5 × 10 × 21 + 20
S = 50 × 21 + 20
S = 1 050 + 20
S = 1 070