Page 109 - Mathematics_Form_3

Sequences and series

(b) Given G = 24, r = 5, n = 10. 2. Find the sum of the first twenty terms
1
n
G ( r − 1) of the geometric series 4 + 8 + 16 + ···

From S = 1 _ ,
n r − 1
substitution of the values into the 3. Find the sum of the first ten terms of
the geometric series 2 − 6 + 18 − 54 + ···
formula gives,
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24( 5 − 1) 4. If the sum of the first n terms of
10

S = __________
10 5 − 1 a geometric progression with the
24 × 9765624 1 __
____________
= first term 1 and the common ratio
4 31 2
___
= 58593744 is , find the number of terms.
16
Therefore, the sum of the first 10 5. If the n term of a geometric
th
terms is 58,593,744. progression is 2 , find the sum of
n
n
G ( r − 1)

(c) From S = 1 _ , it implies the first five terms.

n r − 1
that n 6. If the sum of the first n terms of a
24( 5 − 1)
S = _________ n

n 5 − 1 sequence is 3 − 1, show that the
= 6( 5 − 1) sequence is a geometric progression.
n
Therefore, the formula for the sum 7. Find the sum of the first n terms
of the first n terms of the sequence of each of the following geometric
is S = 6( 5 − 1 ) . series:
n
n
(d) For S > 90000 , it follows that (a) 10 + 50 + 250 + · · ·
n
n
6( 5 − 1 ) > 90000 (b) 1 − 2 + 4 − · · ·

n
5 − 1 > 15000 1 __ 1 __ 1 __
n
8

5 > 15001 (c) + + + · · ·
2
4
Apply logarithm both sides to obtain, 8. The sum of the first 5 terms of a GP
1 ___
1 __
1 __
1 ___
(d) − + − + · · ·
Mathematics for Secondary Schools ⇒> 5.9747 9. The sum of the first n terms of a
27
3
81
9
log 15001
n
log 5 >
n
log 5 log 15001>
⇒
is 124 and the sum of the first 10
log 15001
terms is 4,092. Find the common
n
log 5
ratio.
n
⇒>
)
n
−
geometric progression is ( 51 2 .S =
Therefore, the smallest value of n
n
is 6.
Find the first term and the common
ratio.
Exercise 4.7
progression 2, 2.2, 2.42, 2.662, . . .
1. Given the geometric series 10. How many terms in the geometric
2 + 6 + 18 + · · · Find the sum of will be needed so that the sum of
the first eight terms. the first n terms is greater than 2?
102 Student\s Book Form Three
18/09/2025 09:59:26
MATHEMATIC F3 SB.indd 102
MATHEMATIC F3 SB.indd 102 18/09/2025 09:59:26