急!F6 Arithmetic Sequences 01q9

Question 23
Part a
a+6d=-18...(1)
a+19d=-57....(2)

Solve these equations,
(1)-(2):-13d=39
d=-3

Put d=-3 into (1),
a+6(-3)=-18
a=0

The General Term is (n-1)(-3)

Part (b)
T33=(32)(-3)=-96

Part (c)
T33+T7=(32)(-3)+(6)(-3)=38(-3)
T20=(19)(-3)

Question 21
(a)
1+2+3+....+n>=145
(n+1)*n/2>=145
n^+n-290>=0
n>=16.5 or n<=-17.5 (rejected)
min n = 17

(b)
Part (i)
By using testing method,
17+16+.....+a=145

17+16+....+5=143
17+16+....+5+4=147
So the distribution should be (17, 16, 15,.......5, 2)
There should be 2 cans in the top layer

Part (ii)
2+5+6+7+8+9+10+11
=2+(5+11)/2 *7
=2+8*7
=58
So T33+T7=2(T20)