Matematyka
kotusaga
2017-12-28 14:50:19
Oblicz różnicę i podaj wzór ogólny ciągu arytmetycznego (an). a) a1 = 6 a3 = 20 b) a1 = -4 a4 = 5 c) a1 = 9 a6 = 6 1/2 d) a1 = 13 a10 = - 23
Odpowiedź
damianeeek
2017-12-28 14:59:07

a) [latex] a_1 = 6, a_3 = 20 [/latex] [latex] a_3 = a_1 + 2r [/latex] [latex] 20 = 6 + 2r [/latex] [latex] 14 = 2r [/latex] [latex] r = 7 [/latex] [latex] a_n = a_1 + (n - 1) r [/latex] [latex] a_n = 6 + (n - 1) * 7 [/latex] [latex] a_n = 6 + 7n - 7 [/latex] [latex] a_n = 7n - 1 [/latex] * * * b) [latex] a_1 = -4, a_4 = 5 [/latex] [latex] a_4 = a_1 + 3r [/latex] [latex] 5 = -4 + 3r [/latex] [latex] 9 = 3r [/latex] [latex] r = 3 [/latex] [latex] a_n = a_1 + (n - 1) r [/latex] [latex] a_n = -4 + (n - 1) * 3 [/latex] [latex] a_n = -4 + 3n - 3 [/latex] [latex] a_n = 3n - 7 [/latex] * * * c) [latex] a_1 = 9, a_6 = 6frac{1}{2} [/latex] [latex] a_6 = a_1 + 5r [/latex] [latex] 6frac{1}{2} = 9 + 5r [/latex] [latex] 13 = 18 + 10r [/latex] [latex] -5 = 10r [/latex] [latex] r = -frac{1}{2} [/latex] [latex] a_n = a_1 + (n - 1) r [/latex] [latex] a_n = 9 + (n - 1) * (- frac{1}{2} ) [/latex] [latex] a_n = 9 - frac{1}{2} n + frac{1}{2} [/latex] [latex] a_n = 9frac{1}{2} - frac{1}{2} n [/latex] * * * d) [latex] a_1 = 13, a_10 = -23 [/latex] [latex] a_10 = a_1 + 9r [/latex] [latex] -23 = 13 + 9r [/latex] [latex] -36 = 9r [/latex] [latex] r = -4 [/latex] [latex] a_n = a_1 + (n - 1) r [/latex] [latex] a_n = 13 + (n - 1) * (-4) [/latex] [latex] a_n = 13 - 4n + 4 [/latex] [latex] a_n = 17 - 4n [/latex]

Konto usunięte
2017-12-28 15:00:22

a) a1 = 6 a3 = 20   an = a1 + (n-1)r  a1 = 6   a3 = 20  a3 - a1 = r  20 - 6 = 14/: 2 r = 7  an= 6+ (n-1) * 7 = 6 + 7n - 7 = 7n - 1 b) a1 = -4  a4 = 5   a1 = - 4 a4 =5  a4-a1 = r  5 - (-4) = 9/: 3 r = 3  an = -4(n-1)* 3 = -4+ 3n - 3 = 3n - 7  c) a1 = 9 a6 = 6 1/2  a1 = 9 a6 =  6 1/2 = 6,5  a6 - a1 = r  6,5 - 9 = - 2,5 /:5 r = -0,5  an = 9 + (n-1) * (-0,5) =  9 + (-0,5n) + 0,5 = 9 1/2 - 1/2  d) a1 = 13 a10 = -23  a1 = 13  a10 = -23  a10 - a1 = r  -23 - 13 = -36/: 9  r= -4  an = 13 + (n - 1) * (-4) = 13 + (-4n) + 4 = 17 - 4n 

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