HOW TO FIND FIRST N TERMS FROM THE NTH TERM OF A SEQUENCE
Let an represent the nth term of a sequence.
If you substitute n = 1, you will get the 1st term of the sequence.
If you substitute n = 2, you will get the 1st term of the sequence and so on.
Write the first three terms in the following sequences :
Example 1 :
an = 2n + 5
Solution :
To get the first three terms of the sequence, substitute1 , 2 and 3 for n in an.
|
n = 1 a1 = 2(1) + 5 = 2 + 5 = 7 |
n = 2 a2 = 2(2) + 5 = 4 + 5 = 9 |
n = 3 a3 = 2(3) + 5 = 6 + 5 = 11 |
Hence the 1st three terms of the sequence are 7, 9 and 11 respectively.
Example 2 :
an = (n - 3)/4
Solution :
To get the first three terms of the sequence, substitute1 , 2 and 3 for n in an.
|
n = 1 a1 = (1 - 3)/4 = -2/4 = - 1/2 |
n = 2 a2 = (2 - 3)/4 = -1/4 |
n = 3 a3 = (3 - 3)/4 = 0/4 = 0 |
Hence the 1st three terms of the sequence are -1/2, -1/4 and 0 respectively.
Example 3 :
an = n (n + 2)
Solution :
To get the first three terms of the sequence, substitute1 , 2 and 3 for n in an.
|
n = 1 a1 = 1(1 + 2) = 1 (3) = 3 |
n = 2 a2 = 2 (2 + 2) = 2(4) = 8 |
n = 3 a3 = 3 (3 + 2) = 3(5) = 15 |
Hence the 1st three terms of the sequence are 3, 8 and 15 respectively.
Example 4 :
an = n/(n + 1)
Solution :
To get the first three terms of the sequence, substitute1 , 2 and 3 for n in an.
|
n = 1 a1 = 1/(1 + 1) = 1/2 |
n = 2 a2 = 2/(2 + 1) = 2/3 |
n = 3 a3 = 3/(3 + 1) = 3/4 |
Hence the 1st three terms of the sequence are 1/2, 2/3, and 3/4 respectively.
Example 5 :
an = (2n - 3)/6
Solution :
To get the first three terms of the sequence, substitute1 , 2 and 3 for n in an.
|
n = 1 a1 = (2n - 3)/6 = (2(1) - 3)/6 = (2 - 3)/6 = -1/6 |
n = 2 a2 = (2n - 3)/6 = (2(2) - 3)/6 = (4 - 3)/6 = 1/6 |
n = 3 a3 = 3/(3 + 1) = 3/4 |
Hence the 1st three terms of the sequence are -1/6, 1/6 and 3/4 respectively.
Example 6 :
an = (-1)n-15n+1
Solution :
To get the first three terms of the sequence, substitute1 , 2 and 3 for n in an.
|
n = 1 a1 = (-1)n-1 5n+1 = (-1)1-1 51+1 = (-1)0 52 = 25 |
n = 2 a2 = (-1)n-1 5n+1 = (-1)2-1 52+1 = (-1)1 53 = -125 |
n = 3 a3 = (-1)n-1 5n+1 = (-1)3-1 53+1 = (-1)2 54 = 625 |
Hence the 1st three terms of the sequence are 25, -125 and 625 respectively.
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