Odpowiedź:
1 x + 3x + 5x + 7x + 9x + 11x + 13x + 15x + 17x + 19x = 100x = 75 to
a1 = x, d = r = 2x, n = 10, an = 19x.
Sn = n(a1 + an)/2 = 10(x + 19x)/2 = 10•20x/2 = 100x to
Odpowiedź:
100x = 75 /:100 to x = 75/100 = 3/4 = 0,75
Szczegółowe wyjaśnienie:
x+3x+5x+...+17x+19x-25=50 to x+3x+5x+...+17x+19x = 50 + 25 to
x+3x+5x+...+17x+19x = 75
x(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) = 75 to
x • 100 = 75 to /:100 to x = 75/100 = 3/4 = 0,75
Sprawdzimy tą sumę innym sposobem:
(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) = 100
a1 = 1, różnica ciągu d = r = 2, n = 10, an = 19
Suma n wyrazów ciągu arytmetycznego Sn = n(a1 + an)/2 to
Sn = 10(1 + 19)/2 = 10•20/2 = 100
Obliczymy to jeszcze inaczej:
1 x + 3x + 5x + 7x + 9x + 11x + 13x + 15x + 17x + 19x - 25 = 50 to
1 x + 3x + 5x + 7x + 9x + 11x + 13x + 15x + 17x + 19x = 50 + 25 = 75 to
1 x + 3x + 5x + 7x + 9x + 11x + 13x + 15x + 17x + 19x = 100x = 75 to
a1 = x, d = r = 2x, n = 10, an = 19x.
Sn = n(a1 + an)/2 = 10(x + 19x)/2 = 10•20x/2 = 100x to
Odpowiedź:
100x = 75 /:100 to x = 75/100 = 3/4 = 0,75
