what is the explicit formula for the sequence 3,7,11,15
To find the explicit formula for a sequence, we need to examine the pattern and determine the relationship between the terms.
Looking at the sequence 3, 7, 11, 15, we can observe that each term is obtained by adding 4 to the previous term.
So, the explicit formula for this sequence is:
aₙ = a₁ + (n - 1)d
where aₙ represents the nth term of the sequence, a₁ is the first term, n is the position of the term, and d is the common difference.
In this case, the first term, a₁, is 3, and the common difference, d, is 4. Therefore, the explicit formula for this sequence is:
aₙ = 3 + (n - 1) * 4.
So, to find any term in the sequence, you can substitute the value of n into the formula. For example, if you want to find the 5th term, you would substitute n = 5:
a₅ = 3 + (5 - 1) * 4 = 3 + 4 * 4 = 3 + 16 = 19.
Therefore, the 5th term of the sequence is 19.
To find the explicit formula for a sequence, we need to look for a pattern or relationship between the terms.
In the given sequence 3, 7, 11, 15, we can observe that each term is obtained by adding 4 to the previous term. Notice that 7 = 3 + 4, 11 = 7 + 4, and 15 = 11 + 4.
So, we can express this pattern using an explicit formula. Let's define 'n' as the position of the term in the sequence.
To find the nth term, we can use the formula:
Term(n) = a + (n - 1) * d
Here, 'a' represents the first term of the sequence (in this case, a = 3), and 'd' represents the common difference between each term (d = 4).
Using this formula, we can substitute in the values:
Term(n) = 3 + (n - 1) * 4
Therefore, the explicit formula for the given sequence is:
Term(n) = 3 + 4(n - 1)
Did you notice that there is a "common difference" of 4 ?
so term (n) = .....