急!F6 Geometric Sequences 02q10

(20)

(a)

T(6) = ar^5 = 288 and T(8) = ar^7 = 1152
r^2 = 4
r = 2 or r = -2

for r = 2, a = 9,
thus, the sum of the first 6 terms = 9(2^6 - 1) / (2 - 1) = 567
for r = -2, a = -9,
thus, the sum of the first 6 terms = -9((-2)^6 - 1) / ((-2) - 1) = 189

(b)

for r = -2, a = -9,
thus, the sum of the first 8 terms = -9((-2)^8 - 1) / ((-2) - 1) = 765


(21)

(a)

S(n) = 100(10^n - 1) / (10 - 1) = (100/9)(10^n - 1)

(b)

the sum of the first 7 term of 101, 1001, 10001, ...
= the sum of the first 7 term of 100, 1000, 10000, ... + (1 + 1 + 1 + 1 + 1 + 1 + 1)
= (100/9)(10^7 - 1) + 7
= 111111107