The value of K given the sequence from the question is 18
Data obtained from the question
- Sequence => 6, 15, 24, 33, 42
- Kth term => 159
- Value of K =?
How to determine the type of sequence
To determine the type of sequence, we shall find the difference between each terms
2nd term - 1st term
15 - 6 = 9
3rd term - 2nd term
24 - 15 = 9
4th - 3rd
33 - 24 = 9
5th - 4th
42 - 33 = 9
Since we have a uniform difference between each term by subtracting the 1st from the 2nd and so on, the sequence is arithmetic sequence
How to determine the value of K
- 1st term (a) = 6
- common difference (d) = 9
- nth term = Kth term = 159
- number of term (n) = value of K =?
nth = a + (n - 1)d
159 = 6 + (k - 1)9
Clear bracket
159 = 6 + 9k - 9
159 = 9k - 3
Collect like terms
159 + 3 = 9k
162 = 9k
Divide both side by 9
k = 162 / 9
k = 18
Complete question
The first five terms of a sequence are 6, 15, 24, 33, 42. The Kth term of the sequence is 159. Find the value of k.
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