Question

Rozwiaz rownanie 2+5+8+11+...+x=187

Answer 1

2 + 5 + 8 + 11 + .... + x = 187

 

2, 5, 8, 11, ......, x   ----  ciąg arytmetyczny

 

a1 = 2

r = 5 - 2 = 3

an = x

Sn = 187

 

an = a1 + (n - 1) * r

x = 2 + (n - 1) * 3

x = 2 + 3n - 3

3n = x + 1

n = (x + 1) / 3

 

Sn = [ (a1 + an)/2] * n

187 = [ (2 + x)/2 ] * (x + 1)/3    /*6

1122 = (2 + x)(x + 1)

x² + 2x + 2 + x - 1122 = 0

x² + 3x - 1120 = 0

Δ = 9 + 4 * 1120 = 4489

√Δ = 67

x1 = (-3 - 67)/2 = -70/2 = -35

x2 = (-3 + 67)/2 = 64/2 = 32