Page 16 - Spotlight A+ SPM Additional Mathematics Form 4 & 5
P. 16
Form
4
Chapter 5 Progressions Additional Mathematics
1 3 30. It is given that the sum of the first n terms of a
19. It is given that 6, 7 , 9 , … is a geometric
2 8 geometric progression is S = 3 [3 − 1]. C2
2n
progression. Find the minimum value of n if n 8
the value T > 300. C3 (a) Find the sum of the first 5 terms.
n
(b) Express the n term of the geometric
20. The 2nd and 5th terms of a geometric progression, in term of n.
17
progression are 10 and 19 . Find the first
32 31. Given that the sum of the first n terms of the
term which is more than 100. C3 geometric progression 2, −4, 8, … is 21 846,
find the value of n. C2
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21. Find the sum of first terms of the following
geometric progression. C1 32. It is given the sequence 3, 1, 1 , … is a
(a) 1, 2, 4, …, to n = 13 3
(b) 5, 15, …, to n = 14 geometric progression. Find the value of
(c) 12, –24, 48, …, to n = 12 n when the sum of the first n terms of the
3
2
(d) 3, 3 , 3 , …, to n = 8 29 524
geometric progression is 4 . C2
59 049
7
22. It is given that , –7, 14, … is a geometric
2 33. Determine the value of n when the sum of the CHAP
progression. Find the sum from 3rd term to 8th first n of the geometric progression 125, –25, 5
term of the geometric progression. C2 104
5, … is 104 . C2
625
23. Find the sum from 4th term to 9th term of the
geometric progression 4, –6, 9, … C2 34. It is given that the 2nd term and the 5th
term of a geometric progression are –27 and
24. It is given that 9, –18, 36, … is a geometric 1 respectively. Find C3
progression. Find the sum from 6th term to
18th term of the geometric progression. C2 (a) the first term and the common ratio,
(b) the sum of the first 13 terms,
25. It is given that the nth term of a geometric of the geometric progression.
5
progression is T = – (–2) . Find C2
n
n 35. Given that the 4th term and the 10th term
2
1
(a) the first term and the common ratio, of a geometric progression are –16 and –
(b) the sum of the first 6 terms, respectively. Find C3 4
of the geometric progression.
(a) the first term and the common ratio,
26. Given that the nth term of a geometric (b) the sum from the 5th term to the 12th
progression is T = 3 3 – n , find the sum of the term,
n
first 10 terms. C2 of the geometric progression.
27. It is given that the nth term of a geometric 36. In a geometric progression, the 3rd term and
625 the sum of 4th and 5th term are 60 and 360
progression is T = . Find the sum from
n n respectively. Find C3
5
the 5th term to the 12th term of the geometric (a) the first term and the common ratio,
progression. C2
(b) the sum of the first 11 terms,
of the geometric progression.
28. The sum of the first nth terms of a geometric
2 2n + 1 – 2
progression is given by S = . Find 37. Find the sum to infinity of the following
n
3 C2 geometry progression. C2
(a) the sum of the first 7 terms,
1
(b) the 8th term, (a) 120, 80, 53 , …
of the geometric progression. 3
2 7
(b) 8, 2 , 1 , …
29. Given that the sum of the first nth terms of a 3 9
geometric progression is given by S = 4(2 n – 1 ). (c) 1 , 1 1 , 1 1 2 , …
n
Find C2 5 5 2 5 2
(a) the sum from the 3rd to 7th term, (d) 3x, 1, 1 , …
(b) the nth term of the geometric progression 3x
in terms of n. (in terms of x)
99
