To find the first 5 terms of the sequence, we have apply n = 1, 2, 3, .......in the general rule.
Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference.
Problem 1 :
an = 8 +13n
Solution :
an = 8 +13n
a1 = 8 +13(1) = 8 + 13 a1 = 21 |
a2 = 8 +13(2) = 8 + 26 a2 = 34 |
a3 = 8 +13(3) = 8 + 39 a3 = 47 |
a4 = 8 +13(4) = 8 + 52 a4 = 60 |
a5 = 8 +13(5)
= 8 + 65
a5 = 73
So, first five terms of the sequence is 21, 34, 47, 60, 73.
To find the common difference :
d = a2 – a1 = 34 – 21 = 13
a3 – a2 = 47 – 34 = 13
The sequence is arithmetic because common difference is 13.
Problem 2 :
an = (1/n) +1
Solution :
an = (1/n) +1
a1 = (1/1) +1 a1 = 2 |
a2 = (1/2) +1 a2 = 3/2 |
a3 = (1/3) +1) a3 = 4/3 |
a4 = (1/4) + 1 a4 = 5/4 |
a5 = (1/5) +1)
a5 = 6/5
So, first five terms of the sequence is 2, 3/2, 4/3, 5/4, 6/5.
To find the common difference :
d = a2 – a1 = (3/2) - 2
= (3 - 4)/2
d = -1/2
Problem 3 :
an = 2n + n
Solution :
an = 2n + n
a1 = 21 + 1 = 2 + 1 a1 = 3 |
a2 = 22 + 2 = 4 + 2 a2 = 6 |
a3 = 23 + 3 = 8 + 3 a3 = 11 |
a4 = 24 + 4 = 16 + 4 a4 = 20 |
a5 = 25 + 5 = 32 + 5 a5 = 37 |
So, first five terms of the sequence is 3, 6, 11, 20, 37.
To find the common difference :
d = a2 – a1 = 6 – 3 = 3
a3 – a2 = 11 – 6 = 5
Since the common difference is not same, it is not arithmetic sequence.
Find the first four terms of the sequence given the explicit formula.
Problem 1 :
an = n2 + 3
Solution :
an = n2 + 3
a1 = 12 + 3 = 1 + 3 a1 = 4 |
a2 = 22 + 3 = 4 + 3 a2 = 7 |
a3 = 32 + 3 = 9 + 3 a3 = 12 |
a4 = 42 + 3
= 16 + 3
a4 = 17
So, first four terms of the sequence is 4, 7, 12, 17.
Problem 2 :
an = 15/(n + 3)
Solution :
an = 15/(n + 3)
a1 = 15/(1 + 3) a1 = 15/4 |
a2 = 15/(2 + 3) a2 = 15/5 a2 = 3 |
a3 = 15/(3 + 3) a3 = 15/6 a3 = 5/2 |
a4 = 15/(4 + 3)
a4 = 15/7
a4 = 15/7
So, first four terms of the sequence is 15/4, 3, 5/2, 15/7.
Problem 3 :
an = 2n - 1
Solution :
an = 2n - 1
a1 = 2(1) – 1 = 2 – 1 a1 = 1 |
a2 = 2(2) – 1 = 4 – 1 a2 = 3 |
a3 = 2(3) – 1 = 6 – 1 a3 = 5 |
a4 = 2(4) – 1
= 8 – 1
a4 = 7
So, first four terms of the sequence is 1, 3, 5, 7.
Problem 4 :
an = n/(n +1)
Solution :
an = n/(n +1)
a1 = 1/(1 +1) a1 = 1/2 |
a2 = 2/(2 +1) a2 = 2/3 |
a3 = 3/(3 +1) a3 = 3/4 |
a4 = 4/(4 +1)
a4 = 4/5
So, first four terms of the sequence is 1/2, 2/3, 3/4, 4/5.
Problem 5 :
an = 12 - 3n
Solution :
an = 12 - 3n
a1 = 12 – 3(1) = 12 – 3 a1 = 9 |
a2 = 12 – 3(2) = 12 – 6 a2 = 6 |
a3 = 12 – 3(3) = 12 – 9 a3 = 3 |
a4 = 12 – 3(4)
= 12 – 12
a4 = 0
So, first four terms of the sequence is 9, 6, 3, 0.
Problem 6 :
an = 4n/3
Solution :
an = 4n/3
a1 = 4(1)/3 a1 = 4/3 |
a2 = 4(2)/3 a2 = 8/3 |
a3 = 4(3)/3 a3 = 12/3 a3 = 4 |
a4 = 4(4)/3
a4 = 16/3
So, first four terms of the sequence is 4/3, 8/3, 4, 16/3.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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