急!F6 Arithmetic Sequences 01q6

15.Let d be the common difference .
a1+a2+a3=-12
3{a1+[a1+(3-1)d]}/2=-12
2a1+2d=-8
a1+d=-4.................(1)

a1+a2+...+a5=30
5{a1+[a1+(5-1)d]}/2=30
2a1+4d=12
a1+2d=6................(2)

(2)-(1)=d=10............(3)

Sub (3) into (1),
a1+10=-4
a1=-14

∴First term=-14, common difference=10

T(n)=-14+(n-1)x10=10n-24
T(16)=10x16-24=136
T(40)=10x40-24=376
∴a16+a17+...+a40=(40-16+1)(136+376)/2=6400

17(a) Let a be the first term and d be the common difference.
S(n) is the sum of n terms.

S(10)=10[2a+(10-1)d]/2=220
2a+9d=44............(1)

S(15)=15[2a+(15-1)d]/2=180
2a+14d=24
a+7d=12
a=12-7d................(2)

Sub (2) into (1),
2(12-7d)+9d=44
24-14d+9d=44
5d=-20
d=-4....................(3)

Sub (3) into (2), a=12-7(-4)=40

∴First term=40, common difference=-4

(b) S(k)=k[2(40)+(k-1)(-4)]/2=216
k(80-4k+4)/2=216
k(42-2k)=216
k^2-21k+108=0
(k-12)(k-9)=0
k=9 or k=12