急!F6 Arithmetic Sequences 1q10

16(a) a = 24 and d = 6

Then (n/2)[2a + (n - 1)d] = 360

n(48 + 6n - 6) = 720

6n^2 + 42n - 720 = 0

3n^2 + 21n - 360 = 0

(3n + 45)(n - 8) = 0

n = -15 or 8

So, the number of sides is 8

(b) The largest angle = a + (n - 1)d = 24 + 7 * 6 = 24 + 42 = 66

18(a) a = 0.8, d = 0.05

Let 0.8 + 0.05(n - 1) = 1.75

n = 20

So, 20 tiles are used

(b) Length of the path

= (20/2)(2 * 0.8 + 0.05 * (20 - 1))

= 25.5

(c) The width of the path

= a + 4d

= 0.8 + 4 * 0.05

= 1

(d) The area of the path is 25.5 m^2