Question

3. Så se rezolve ecuațiile:
a) 1+ 4 +7+ ... + x = 117;
b) 1 +8+15+ ... + x = 3075;
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Answer 1

Răspuns:

a)1+4+7+....+x=117

2+((n-1) ×3)/ ×n=117

(-1+3n) ×n=234

3n²-n-234=0

Δ=532

N=9

x=a1+8r=25

x=25

 

b) 1+8+15+....+x=3075

1+(1+7)+(1+7×2)+....+x=3075

x=1+7n

1+(1+7)+(1+7×2)+....+(1+7n)=3075

1×(n+1)+7(1+2+....+n)=3075

n+1+7×n×(n+1)/2=3075

2n+2+7n²+7n=6150

7n²+9n-6148=0

7n²-203n+212n-6148=0

7n(n-29)+212(n-29)=0

(n-29)(7n+212)=0

n=29  

x=1+7×29=204

x = 204