Final answer:
The nth term of the sequence 11, -689, -1389, -2089, -2789 is found by using the arithmetic sequence formula, resulting in an = 711 - 700n.
Step-by-step explanation:
To find the nth term of the sequence 11, -689, -1389, -2089, -2789, we need to determine the pattern or rule that defines the sequence. First, observe the difference between each term:
- From 11 to -689, the difference is -700.
- From -689 to -1389, the difference is -700.
- From -1389 to -2089, the difference is -700.
- From -2089 to -2789, the difference also is -700.
Since the difference between consecutive terms is constant, this sequence is an arithmetic sequence. The common difference (d) is -700. The first term (a1) of the sequence is 11. To find the nth term (an) of an arithmetic sequence, we use the formula:
an = a1 + (n - 1) × d
Plugging in the values, we get:
an = 11 + (n - 1) × (-700)
Simplifying the equation:
an = 11 - 700n + 700
Which further simplifies to:
an = 711 - 700n
Therefore, the nth term of the given sequence is 711 - 700n.