Question

What is a descending arithmetic sequence?

Answer 1

Hint: We can understand that descending means larger to smaller. But there is a difference between descending sequence and descending arithmetic sequence. Descending arithmetic sequence is nothing but the descending sequence of numbers which has a constant difference between each of the numbers in the complete list.

Complete step by step solution:
Let's take a closer look at arithmetic sequences. An arithmetic series is a collection of numbers that follow a set pattern. There are four different kinds of sequences. There are four types of series: arithmetic, geometric, harmonic, and Fibonacci. The Fibonacci sequence is the most well-known.
Let's look at some examples of descending arithmetic sequences.
\[12,9,6,3,0,-3,-6\]
From the above series, let us find out the constant difference first. In order to find out the difference , let us check out the difference between the \[{{1}^{st}}\] and the \[{{2}^{nd}}\] term and then the difference between \[{{2}^{nd}}\] and the \[{{3}^{rd}}\] term. It can be either from the beginning of the series or from the end of the series. We can also check it for the entire series.
We can find that \[12-9=3\] and \[9-6=3\].
\[\therefore \] The constant difference is \[3\] and the list is in descending order.
Hence the considered list is a descending arithmetic sequence.

Note: These sequences can be finite or infinite. In the infinite list, the sequence goes up to \[{{n}^{th}}\] term. In order to find the \[{{n}^{th}}\] term, the formula is \[{{a}_{n}}=dn+c\]. Using this formula, we can find the desired term from the first till the \[{{n}^{th}}\].