急!F6 Arithmetic Sequences 1q11

17.
(a)
Let a and d be the first term and the common difference respectively.

T3 :
a + 2d = -22 ...... [1]

T5 + T9 :
(a + 4d) + (a + 8d) = -4
2a + 12d = -4
a + 6d = -2 ...... [2]

[2] - [1] :
4d = 20
d = 5

Put d = 5 into [1] :
a + 2(5) = -22
a = -32

Hence, Tn = -32 + 5(n - 1)= 5n - 37

(b)
Tn > 0
5n - 37 > 0
5n > 37
n > 7.4

The first positive term is the 8thterm
= 5(8) - 37
= 3


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18.
(a)
T1 = 1 = 1²
T­2 = 4 = 2²
T3 = 9 = 3²
T4 = 16 = 4²
T5 = 25 = 5²

Hence, Tn = n²

(b)
Un = Tn+1 - Tn
= (n + 1)² -n²
= n² +2n + 1 - n²
= 2n + 1

(c)
U1, U­2, U3, ......, Un
= 3, 5, 7, ......, 2n+1
= 3, 3+2, 3+2*2, ......, 3+(n-1)*2

Then, Un is the general term of anarithmetic sequence,
with the first term = 3 and the common difference = 2.