Question

se considera sirul : 8; 15 ; 22 ; 29 ; 36 .... a)pe ce loc se afla nr 1513 b) calculati suma : S = 8+15+22+29+...+1513

Answer 1

progresie atmetica

a₁ = 8; r = 7 ==> an = a₁ + ( n - 1) x r

8 + ( n - 1 ) x 7 = 1 513

( n - 1 ) x 7 = 1 513 - 8 = 1 505

n - 1 = 1 505 : 7

n - 1 = 215

n = 215 + 1 = 216 → pozitia pe care se gaseste numarul 1 513

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b)

S = 8 + 15 + 22 + 28 + ....... + 1513

→ aflam cati termeni are suma

( 1 513 - 8 ) : 7 + 1 = 1 505 : 7 + 1 = 215 + 1 = 216 termeni are suma

S = 216 x ( 8 + 1 513 ) / 2

S = 108 x 1 521

S = 164 268