Question

Daca se cunoscdoi termeni ai unei progresii geometrice Bn: a) B3=6 ,B5 =24,sa se gaseasca B7 ,B9 B10 ;B3=B1*q la puterea 2​

Answer 1

b3 = b1 × q^2 = 6

b5 = b1 × q^4 = 24

Dar b1 × q^4 = b1 × q^2 × q^2 = 6 × q^2 = 24 => q^2 = 24 : 6 = 4 = 2^2 => q = 2

Dar b1 × q^2 = 6, adica b1 × 4 = 6 => b1 = 6/4 = 3/2

Calculăm b7, b9, b10:

b7 = b1 × q^6 = (3/2) × 2^6 = 3 × 2^5 = 3 × 32 = 96

b9 = b1 × q^8 = (3/2) × 2^8 = 3 × 2^7 = 3 × 128 = 384

b10 = b9 × q = 384 × 2 = 768