急 F6 Geometric Sequences 02q15

34.
(a)
F(x) = x⁴ - 8x³ + 14x² + 8x - 15

F(3)
= (3)⁴ - 8(3)³ + 14(3)² + 8(3) - 15
= 81 - 216 + 126 + 24 - 15
0

Hence, F(3) = 0

(b)
F(3) = 0
x - 3 is a factor of F(x).

F(5) = (5)⁴ - 8(5)³ + 14(5)² + 8(5) - 15 = 0
x - 5 is a factor of F(x).

F(1) = (1)⁴ - 8(1)³ + 14(1)² + 8(1) - 15 = 0
x - 1 is a factor of F(x).

F(-1) = (-1)⁴ - 8(-1)³ + 14(-1)² + 8(-1) - 15 = 0
x + 1 is a factor of F(x).

Hence, F(x) = (x + 1)(x - 1)(x + 3)(x + 5)

F(x) = 0
(x + 1)(x - 1)(x + 3)(x + 5) = 0
x = -1 or x = 1 or x = 3 or x = 5


35.
(a)
General term Tn = log arⁿ⁻¹

(b)
log a, log ar, log ar², ...... log arⁿ⁻¹
= log a, log a + log r, log a + log r², ....., log a + log rⁿ⁻¹
= log a, log a + (log r), log a + 2(log r), ....., log a + (n - 1)(log r)

it is an arithmetic sequence.

(c)
Common difference, Tn+1 - Tn
= log arⁿ - log arⁿ⁻¹
= log (arⁿ / arⁿ⁻¹)
= log r

(d)
Sum of the first 20 terms, S20
= 20 x [2 log a + (20 - 1) log r] / 2
= 20 log a + 190 log r
= 20 log 0.01 + 190 log 10
= 150