How do you write an equation for the nth term of the arithmetic sequence: -3, -5, -7, -9, ...?

Question

HIX Tutor · Accepted Answer

undefined To write an equation for the nth term of an arithmetic sequence, you can use the formula: nth term = first term + (n - 1) * common difference.
For the given arithmetic sequence: -3, -5, -7, -9, ...
The first term is -3.
The common difference is -2 (each term decreases by 2).
To find the nth term, you can replace the first term and the common difference in the formula.
So, the equation for the nth term of this arithmetic sequence is: nth term = -3 + (n - 1) * (-2).

Anna Allen · Answer

#a_n=-2n-1# The formula for an arithmetic sequence is #a_n=a_1 +(n-1)d# where #a_1# is the first term and #d# is the difference between terms. In this case #a_1=-3# and #d=-2# #a_n=-3+(n-1)(-2)=-3-2n+2 =-2n-1# #a_n=-2n-1#

Elias Ackerman · Answer

undefined The nth term $ a_n $ of an arithmetic sequence can be represented by the formula:

$$ a_n = a_1 + (n - 1) \cdot d $$

Where:
- $ a_n $ is the nth term,
- $ a_1 $ is the first term of the sequence,
- $ n $ is the term number,
- $ d $ is the common difference between consecutive terms.

In the given sequence: -3, -5, -7, -9, ..., the first term ($ a_1 $) is -3, and the common difference ($ d $) is -2 (since each term decreases by 2).

Substituting the values into the formula:

$$ a_n = -3 + (n - 1) \cdot (-2) $$

So, the equation for the nth term of the arithmetic sequence is:

$$ a_n = -3 - 2(n - 1) $$