Write the Explicit Formula for the given sequence.
-16, -9, -2, 5, 12, ...
x + 7
term(n) = 7x - 23 , where x is a whole number
To find the explicit formula for a given sequence, we need to first determine the pattern or rule followed by the sequence. Looking at the sequence: -16, -9, -2, 5, 12, ... we notice that each term is increasing by 7 compared to the previous term.
Therefore, the pattern or rule for this sequence is to add 7 to each term to get the next term.
To express this pattern algebraically, we can write the explicit formula as:
Term(n) = -16 + 7(n - 1)
Here, Term(n) represents the value of the nth term in the sequence. In this case, n starts from 1 (since the first term is -16), and we subtract 1 from n since the pattern starts with adding 7 to the first term to get the second term, and so on.
So, if we want to find the value of the 10th term, we can substitute n = 10 into the formula:
Term(10) = -16 + 7(10 - 1)
= -16 + 7(9)
= -16 + 63
= 47
Thus, the 10th term in the sequence is 47.