Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
My answer is 15, 30, 45, 60, 75 I don't know how to do the rest please help.
write a recursive formula for the sequence 14,10 6,2
a_1 = 14
a_n = a_(n-1) - 4
To find the explicit and recursive formulas for a given sequence, we need to first analyze the pattern formed by the terms.
Looking at the given sequence {15, 30, 45, 60, 75}, it appears that each term is obtained by multiplying the previous term by a constant value of 15. So, we can conclude that this sequence follows a linear pattern.
To find the explicit formula, we can use the general formula for an arithmetic sequence, which is given by:
an = a1 + (n-1)d
where:
an represents the nth term of the sequence,
a1 represents the first term of the sequence,
n represents the position of the term in the sequence, and
d represents the common difference between the terms.
Now, let's apply this formula to our sequence:
a1 = 15 (since it is the first term)
d = 30 - 15 = 15 (difference between the first two terms)
Using the formula, we get:
an = 15 + (n-1)15
= 15 + 15n - 15
= 15n
Therefore, the explicit formula for the given sequence is an = 15n.
To find the recursive formula, we can look at how each term is related to the previous term. In this case, each term is obtained by adding a constant value of 15 to the previous term.
Using recursive notation, we can express this as follows:
a(1) = 15 (first term)
a(n) = a(n-1) + 15
So, the recursive formula for the given sequence is:
a(1) = 15
a(n) = a(n-1) + 15
By using these formulas, we can find any term in the sequence by substituting the value of n. For example, to find the 10th term, we substitute n = 10 in the explicit formula:
a(10) = 15(10) = 150
Therefore, the 10th term in the sequence is 150.
a_n = 15n
a_1 = 15
a_n+1 = a_n + 15