Question

CALCULEAZĂ SUMELE:
S=4+7+10+?+91=
S=6+11+16+21+?+101=

Answer 1

a) S = 4+7+10+...+91
Este un sir din 3 in 3 format din numere care dau restul 1 la impartirea la 3
S = 3×1+1 + 3×2+1 + 3×3+1 + ... + 3×30+1
= 3×1 + 3×2 + 3×3 + ... + 3×30 + 1+1+1+...+1
= 3×(1+2+3+...+30) + 30
= 3×30×31:2 + 30
= 90×31:2 + 30
= 2790:2 + 30
= 1395 + 30 = 1425

b) S = 6+11+16+...+101
Un sir din 5 in 5 cu numere care dau restul 1 la impartirea la 5
S = 5×1+1 + 5×2+1 + 5×3+1 + ... + 5×20+1
= 5×1 + 5×2 + 5×3 + ... + 5×20 + 1+1+1+...+1
= 5×(1+2+3+...+20) + 20
= 5×20×21:2 + 20
= 100×21:2 + 20
= 2100:2 + 20
= 1050+20 = 1070

Answer 2

S = 4+7+10+...+91
aflam cati termeni are suma
(91 - 4) : 3 + 1 = 87:3+1 = 29+1 = 30
S = (4+91) × 30 : 2
S = 95 × 15
S = 1 425

S = 6 + 11 + 16 + 21 +...+ 101
aflam cati termeni are suma
(101 -6) : 5 + 1 = 95:5 + 1 = 19+1 = 20
S = (6+101)× 20 : 2
S = 107 × 10
S = 1 070