Odpowiedź:
z.10
4,7,10, ... , x to ciąg arytmetyczny
a1 = 4 r = 3
an = x Sn = 424
Mamy
x = an = a1 + ( n - 1)*3 = 4 + 3 n - 3 =3 n + 1
oraz Sn = [tex]\frac{a1 + an}{2}[/tex] *n
więc
[tex]\frac{4 + x}{2} *n[/tex] = 424 ⇒ ( 4 + x)*n = 848
( 4 + 3 n + 1)*n = 848
( 5 + 3n)*n = 848
3 n² + 5 n - 848 = 0
Δ = 5² -4*3*(-848) = 25 + 10 176 = 10 201
√Δ = 101
zatem
n = [tex]\frac{- 5 - 101}{6}[/tex] - odpada lub n = [tex]\frac{-5 + 101}{6}[/tex] = 16
x = 3 n + 1 = 3*16 + 1 = 49
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z.11
3, x1,x2,x3, 768 - ciąg geometryczny
więc mamy
a1 = 3
x1 = 3*q
x2 = 3*q²
x3 = 3*q³
x4 = 3*q^4 = 768
3*q^4 = 768 / : 3
q^4 = 256
q² = √256 = 16
q = -4 lub q = 4
zatem:
x1 = 3*(-4) = - 12
x2 = -12*(-4) = 48
x3 = 48*(-4) = - 192
lub
x1 = 3*4 = 12
x2 = 12*4 = 48
x3 = 48*4 = 192
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Szczegółowe wyjaśnienie:
