1) b1=-32, q=1,2 найти b7=? 2) b1=2, q=6 найти S6=? 3) S9=?, b2=0,04, b4=0,16 4) найти b1=? если q=3, S4=560

1) b7=b1*q^6=-32 * (1/2) ^6 = - 32*1/64 = -1/2

2) Sn = b1 * (1-q^n) / (1-q)

S6 = 2 * (1-6^6) / (1-6) = 2 * (1-46656) / (-5) = 2 * (-46655) / (-5) = 18662.

3) b4 = b2*q^2

q^2 = b4/b2 = 0.16/0.04 = 4, q = ± √4 = ±2

b2 = b1*q, b1=b2/q

Если q = 2, b1=0.04/2 = 0.02; S9 = 0.02 * (1-2^9) / (1-2) = 0.02 * (1-512) / (-1) = 0.02*511 = 10.22

Если q = - 2, b1=0.04 / (-2) = - 0.02; S9 = - 0.02 * (1+2^9) / (1+2) = - 0.02*513/3 = - 3.42

4) S4 = b1 * (1 - q^4) / (1-q)

560 = b1 * (1-3^4) / (1-3)

560=b1 * (-80) / (-2)

560 = b1*40

b1=560/40

b1 = 14.