4 krótkie zadanka z "ciągów arytmetycznych i geometrycznych" PROSZE O POMOC ;< HAŁA MISTRZ!: 1.Oblicz sumę wszystkich dwucyfrowych licz naturalnych ktore przy dzieleniu przez 7 daja liczbe 1 ```````````````````````````````````````````````````````````````````````````` `````````````````````````````````````````````````````````````` 2. Liczby 3 i 7 sa dwoma poczatkowymi wyrazami rosnoacego ciagu arytmetycznego. Oblicz sume tego ciagu od 11 do 30 ```````````````````````````````````````````````````````````````````````````` `````````````````````````````````````````````````````````````` 3. Oblicz pierwszy wyraz (a₁) i iloraz (q) wiedzac ze a₂=36 i a₅=4,5. Oblicz sume 10 pocatkowych wyrazow tego ciagu (S₁0_ ``````````````````````````````````````````````````````````````````````````` ``````````````````````````````````````````````````````````````` 4. Oblicz równanie 13+11+0+...+x=51

Godzio: 1. Po raz setny : liczby dwucyfrowe: 10, 11, 12, ..., 99 dwucyfrowe które przy dzieleniu przez 7 dają liczbę 1: 15,22,29, ...., 99 Suma tych liczb: 15 + 22 + 29 + ... + 99 a₁ = 15 a_n = 99 r = 7 a_n = a₁ + (n−1)*r 99 = 15 + 7n − 7 99 = 8 + 7n 91 = 7n n = 13

	a1 + an
Sn =		* n = ...
	2

2. a₁ = 3 a₂ = 7 r = a₂ − a₁ = 4 a₁1 = a₁ + 10r = 3 + 40 = 43 a₃₀ = a₁ + 29r = 3 + 116 = 119 n = ? −> a₁1,a₁₂, a₁3, .... a₃₀ => n = 20

	a11 + a30
S11−>30 =		* 20 = ...
	2

3.

a5
	= q3
a2

4,5
	= q3
36

1
	= q3
8

	1
q =
	2

a₂ = a₁ * q

	1
36 = a1 *
	2

a₁ = 72

	1 − q10
S10 = a1 *		= ... podstaw dane i oblicz
	1 − q

4. 13 + 11 + 9 + ... + x = 51 a₁ = 13 a_n = x r = − 2 S_n = 51 a_n = a₁ + (n−1)*r x = 13 − 2n + 3 x = 16 − 2n

	a1 + an		13 + x		29 − 2n
Sn =		* n =		* n =		* n
	2		2		2

29 − 2n
	* n = 51
2

29n − 2n² = 102 −2n² + 29n − 102 = 0 Δ = 25

	−29 − 5		−34
n1 =		=		−> niecałkowita więc odrzucamy
	−4		−4

	−29 +5
n2 =		= 6
	−4

n = 6 x = 16 − 2n = 16 − 12 = 4

Menia;): W ciagu geometrycznym a4=8,a7=64.oblicz a1 i q tego ciagu. Prosze o pomoc

krystek: https://matematykaszkolna.pl/strona/279.html

Ajtek: a₄=a₁*q³ a₇=a₁*q⁶ Podstaw i policz, jak coś to pomogę .

Ajtek: Witaj krystek .

krystek: Witaj Ajtek do jutra!

Ajtek: Spokojnej nocki w takim razie