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6. Find the 9 th term of the arithmetic sequence $-5 x-8,-8 x-13,-11 x-18, \ldots$
Answer
Final Answer: The 9th term of the arithmetic sequence is \(\boxed{-29x - 48}\).
Step 1 ：The given sequence is an arithmetic sequence. In an arithmetic sequence, the difference between any two successive terms is constant. This constant difference is also known as the common difference of the arithmetic sequence.
Step 2 ：The general form of an arithmetic sequence can be written as: a, a+d, a+2d, a+3d, ..., a+(n-1)d, where 'a' is the first term, 'd' is the common difference and 'n' is the term number.
Step 3 ：In this case, we can see that the common difference 'd' is \(-3x-5\). The first term 'a' is \(-5x-8\). We are asked to find the 9th term of the sequence, so n=9.
Step 4 ：We can use the formula for the nth term of an arithmetic sequence, which is: a+(n-1)d.
Step 5 ：Substituting the values we have: a = \(-5x - 8\), d = \(-3x - 5\), and n = 9, into the formula, we get the 9th term of the arithmetic sequence as \(-29x - 48\).
Step 6 ：Final Answer: The 9th term of the arithmetic sequence is \(\boxed{-29x - 48}\).
