Question

Determina primul termen si ratia progresiei geometrice (bn) daca
b4-b1=14
S3=14

Answer 1

b4-b1=14 
b4=b1*q^3
b4-b1=14 ->
b1*q^3-b1=14
b1(q^3-1)=14
S3=14 ->>>
b1(q^3-1)/q-1=14
b1(q^3-1)=14q-14
 Avem ecuatia 1 ->>b1(q^3-1)=14
Si ecuatia 2->b1(q^3-1)=14q-14
Impartim ecuatia 1 la ecuatia 2 ->>>
Si obtinem  1=14/14q-14
1=14/14(q-1)
1=1/q-1
q-1=1
q=2 avem ratia 2 .
Ne intoarcem in ecuatia 1 si inlocuim q=2 
Ecuatia 1 :b1(q^3-1)=14
7b1=14
b1=14/7
b1=2  
Deci b1=q=2
b4-b1=14 ->>> b1*q^3-b1=2*8-2=16-2=14. Adv!
Deci valorile sunt corecte.