In the arithmetic sequence -7, -4, -1, 2,..., what term is 44?
clearly, a=-7 and d=3
-7+(n-1)*3=44
Now just find n.
In the arithmetic sequence -7,-4,-1,2 which term is 44?
To determine the term that corresponds to the number 44 in the arithmetic sequence -7, -4, -1, 2,..., we can use the formula for the nth term of an arithmetic sequence.
The formula is: aₙ = a₁ + (n - 1) * d
Where:
aₙ represents the nth term,
a₁ is the first term, and
d is the common difference.
In this case, the first term (a₁) is -7, and the common difference (d) is 3 (since we are adding 3 to each term to get to the next term).
Let's substitute these values into the formula and solve for n:
44 = -7 + (n - 1) * 3
To isolate n, let's simplify the equation:
44 = -7 + 3n - 3
Combine like terms:
44 + 7 - 3 = 3n
44 + 4 = 3n
48 = 3n
Now, divide both sides of the equation by 3:
48 / 3 = n
16 = n
Therefore, the term that corresponds to the number 44 is the 16th term in the given arithmetic sequence.
To find the term that corresponds to a given value in an arithmetic sequence, you can use the formula for the nth term of an arithmetic sequence.
The formula for the nth term of an arithmetic sequence is: an = a1 + (n - 1)d
Here's how you can apply this formula to find which term corresponds to the value 44 in the given arithmetic sequence:
Step 1: Identify the first term (a1) and the common difference (d).
In the given sequence, the first term is -7, and the common difference is 3.
Step 2: Plug the given values into the formula.
an = -7 + (n - 1)3
Step 3: Set up an equation and solve for n.
-7 + 3n - 3 = 44
3n - 10 = 44
3n = 54
n = 18
Therefore, the term that corresponds to the value 44 in the arithmetic sequence -7, -4, -1, 2, ... is the 18th term.