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3
22. (a) 10 1 2 n – 1 [1] a = −780
4
60
(–780 + l)
S =
2
3
(b) 10 1 2 n – 1 . 0 60 = 9840
4
3
log 3 10 + log 3 1 2 n – 1 = 0 l = 1108 [4]
4 4 4
2
log 3 10 + (n – 1) = 0 26. T = a + (2 − 1)d = 5x + 17x + 2
2
4 n = 1 – log 3 10 25x + 50 = 5x + 17x + 2
2
= 9 4 x = −2.4 and x = 4
[2] When x = −2.4,
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23. r = 0.8 = 2 T = a + 2d
3
0.4 = 25(−2.4) + 2(50)
0.4(1 – 2 ) . 125000 = 40
n
1 – 2
n = log 312501 = 18.253… When x = 4,
2
n = 19 T = a + 2d
3
[3] = 25(4) + 2(50)
= 200
24. (a) T = ar = 8 [4]
2
a = 8
5
r 27. (3 + x)
5
5
5
3 2
4
T = ar = 4(x + 1) = 3 + C (3) (x) + C (3) x
2
2
1
3
2
a = 4(x + 1) = 243 + 405x + 270x
r 2
2 5
8 4(x + 1) (3 + x − x )
=
r r 2 = [3 + (x − x )]
2
5
2 2
2
r = (x + 1) = 243 + 405(x − x ) + 270(x − x )
2 = 243 + 405x − 405x + 270(x − 2x + x )
2
2
3
4
8
a = = −405x + 270x + …
2
2
(x + 1)
2
2 = −135x + … [4]
= 16
x + 1 [4] 28. a + 2d = ar
a + 8d = ar
2
3
a(1 – r ) ar − a = 2d
(b) S = 1 – r = 28 ar – ar = 6d
2
3
ar – ar = 3ar – 3a
2
3
1 16 21 1 x + 1 2 2 ar – 4ar + 3a = 0
1 –
2
x + 1 2 = 28 r = 3 or r = 1 (rejected)
1 – 1 x + 1 2 3a – a = 2d
2
x – 4x + 3x = 0 2a = 2d
2
3
x = 0, 1, 3 a = d
x = 3 only ar – a = 2a
[4] ar = 3a
(c) T = ar r = 3
27
28
= 4(2)
27
= 536870912 a + 2d = 3a
[2] d = 1, a = 1
1 1 2 2
5
6561 1 – 1 8 S = 1(3 – 1)
25. S = 3 5 3 – 1
8
1 – 1 = 121
3
= 9840 [7]
S = 60 (2a + 59(32))
60 2
= 9840
Answers 197
Answers Add Math.indd 197 14/03/2022 12:29 PM