WRITE THE FIRST FIVE TERMS OF THE SEQUENCE
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Write down the first five terms of the sequence given by :
Example 1 :
un = 2n - 1
Solution :
We need to find the first five terms
That is, u1, u2, u3, u4, u5
un = 2n – 1
|
When n = 1 u1 = 2(1) - 1 u1 = 2 - 1 u1 = 1 |
When n = 2 u2 = 2(2) - 1 u2 = 4 - 1 u2 = 3 |
|
When n = 3 u3 = 2(3) - 1 u3 = 6 - 1 u3 = 5 |
When n = 4 u4 = 2(4) - 1 u4 = 8 - 1 u4 = 7 |
When n = 5
u5 = 2(5) - 1
u5 = 10 - 1
u5 = 9
Hence, the first five terms are 1, 3, 5, 7, 9,……
Example 2 :
un = 2n + 5
Solution :
We need to find the first five terms
That is, u1, u2, u3, u4, u5
un = 2n + 5
|
When n = 1 u1 = 2(1) + 5 u1 = 2 + 5 u1 = 7 |
When n = 2 u2 = 2(2) + 5 u2 = 4 + 5
u2
= 9 |
|
When n = 3 u3 = 2(3) + 5 u3 = 6 + 5 u3 = 11 |
When n = 4 u4 = 2(4) + 5 u4 = 8 + 5 u4 = 13 |
When n = 5
u5 = 2(5) + 5
u5 = 10 + 5
u5 = 15
Hence, the first five terms are 7, 9, 11, 13, 15,……
Example 3 :
un = 5n + 1
Solution :
We need to find the first five terms
That is, u1, u2, u3, u4, u5
un = 5n + 1
|
When n = 1 u1 = 5(1) + 1 u1 = 5 + 1 u1 = 6 |
When n = 2 u2 = 5(2) + 1 u2 = 10 + 1 u2 = 11 |
|
When n = 3 u3 = 5(3) + 1 u3 = 15 + 1 u3 = 16 |
When n = 4 u4 = 5(4) + 1 u4 = 20 + 1 u4 = 21 |
When n = 5
u5 = 5(5) + 1
u5 = 25 + 1
u5 = 26
Hence, the first five terms are 6, 11, 16, 21, 26,……
Example 4 :
un = 7n + 2
Solution :
We need to find the first five terms
That is, u1, u2, u3, u4, u5
un = 7n + 2
|
When n = 1 u1 = 7(1) + 2 u1 = 7 + 2 u1 = 9 |
When n = 2 u2 = 7(2) + 2 u2 = 14 + 2 u2 = 16 |
|
When n = 3 u3 = 7(3) + 2 u3 = 21 + 2 u3 = 23 |
When n = 4 u4 = 7(4) + 2 u4 = 28 + 2 u4 = 30 |
When n = 5
u5 = 7(5) + 2
u5 = 35 + 2
u5 = 37
Hence, the first five terms are 9, 16, 23, 30, 37,……
Example 5 :
un = - 2n + 5
Solution :
We need to find the first five terms
That is, u1, u2, u3, u4, u5
un = - 2n + 5
|
When n = 1 u1 = - 2(1) + 5 u1 = - 2 + 5 u1 = 3 |
When n = 2 u2 = - 2(2) + 5 u2 = - 4 + 5 u2 = 1 |
|
When n = 3 u3 = - 2(3) + 5 u3 = - 6 + 5 u3 = - 1 |
When n = 4 u4 = - 2(4) + 5 u4 = - 8 + 5 u4 = - 3 |
When n = 5
u5 = -2(5) + 5
u5 = - 10 + 5
u5 = - 5
Hence, the first five terms are 3, 1, - 1, - 3, - 5,……
Example 6 :
un = - 3n + 4
Solution :
We need to find the first five terms
That is, u1, u2, u3, u4, u5
un = - 3n + 4
|
When n = 1 u1 = - 3(1) + 4 u1 = - 3 + 4 u1 = 1 |
When n = 2 u2 = - 3(2) + 4 u2 = - 6 + 4 u2 = - 2 |
|
When n = 3 u3 = - 3(3) + 4 u3 = - 9 + 4 u3 = - 5 |
When n = 4 u4 = - 3(4) + 4 u4 = - 12 + 4 u4 = - 8 |
When n = 5
u5 = - 3(5) + 4
u5 = - 15 + 4
u5 = - 11
Hence, the first five terms are 1, - 2, - 5, - 8, - 11,……
Example 7 :
A sequence has first term 20 and the difference between the terms is always 31.
a) Determine a formula to generate the terms of the sequence
b) Calculate the first 5 terms of the sequence.
Solution :
i) First term (a) = 21
Difference between the terms
= common difference (d) = 31
tn = a + (n - 1) d
tn = 21 + (n - 1) (31)
= 21 + 31n - 31
= -10 + 31n
So, the required formula is 31n - 10
ii) When n = 5
t5 = -10 + 31(5)
= -10 + 155
= 145
First five terms are
21, 52, 83, 114, 145
Example 8 :
The second and third terms of the sequence are 16 and 27. The difference between successive terms in the sequence is always constant.
a) Determine the general formula of the sequence.
b) Calculate the first 5 terms of the sequence.
Solution :
a) Second term = 16
third term = 27
a + d = 16 ------(1)
a + 2d = 27 -----(2)
(1) - (2)
d - 2d = 16 - 27
-d = -11
d = 11
Applying the value of d in (1), we get
a + 11 = 16
a = 16 - 11
a = 5
General formula :
tn = a + (n - 1) d
tn = 5 + (n - 1)11
= 5 + 11n - 11
tn = -6 + 11n
b) When n = 1
t1 = -6 + 11(1) ==> 5
When n = 2
t2 = -6 + 11(2) ==> 16
When n = 3
t3 = -6 + 11(3) ==> 27
When n = 4
t4 = -6 + 11(4) ==> 38
When n = 5
t5 = -6 + 11(5) ==> 49
So, the first 5 terms are 5, 16, 27, 38, 49
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