If the difference of an arithmetic sequence is 4 and the 5th term is 15.what is the first term of the sequence?
Generally called the "common difference" of 4 ---> d = 4
term(5) = a + 4d
a+4(4) = 15
a = 15-16 = -1<---- first term
To find the first term of the arithmetic sequence, you can use the formula:
\(a_1 = a_n - (n-1)d\)
where:
\(a_1\) is the first term,
\(a_n\) is the \(n\)th term, and
\(d\) is the common difference in the sequence.
We are given that the common difference (\(d\)) is 4 and the 5th term (\(a_5\)) is 15.
So, substituting these values into the formula, we have:
\(a_1 = 15 - (5-1)(4)\)
Simplifying the expression:
\(a_1 = 15 - 4(4)\)
\(a_1 = 15 - 16\)
\(a_1 = -1\)
Therefore, the first term of the sequence is -1.
To find the first term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
An = A1 + (n - 1)d
where An represents the nth term, A1 represents the first term, n represents the position of the term in the sequence, and d represents the common difference.
Given that the difference of the arithmetic sequence is 4, we have:
d = 4
To find the first term, we need to find the value of A1. Using the given information that the 5th term is 15, we can substitute the values into the formula:
A5 = A1 + (5 - 1)d
15 = A1 + 4(5 - 1)
15 = A1 + 4(4)
15 = A1 + 16
Subtracting 16 from both sides of the equation, we get:
-1 = A1
Therefore, the first term of the arithmetic sequence is -1.