What is the nth term rule of the linear sequence below? − 4 , − 1 , 2 , 5 , 8
clearly,
a = -4
d = 3
so now you can write the formula as usual, right?
3n +4
To find the nth term rule of a linear sequence, we need to look for a pattern in the sequence. In a linear sequence, the difference between consecutive terms is constant.
Let's examine the given sequence: −4, −1, 2, 5, 8.
To find the difference between consecutive terms, we subtract each term from its previous term:
−1 - (-4) = 3
2 - (-1) = 3
5 - 2 = 3
8 - 5 = 3
We observe that the difference between consecutive terms is 3. This means that the sequence has a common difference of 3.
Now, to find the nth term rule, we need the first term of the sequence. In this case, the first term is −4.
The nth term rule for a linear sequence is given by:
nth term = first term + (n - 1) * common difference
Substituting the values we found, the nth term rule for the given sequence is:
nth term = -4 + (n - 1) * 3
So, the nth term rule of the given linear sequence is -4 + (n - 1) * 3.