Question Video: Writing the Terms of a Sequence given the Value of Its First Term Mathematics

Write the first six terms of the sequence of negative odd numbers starting from −1.

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Video Transcript

Write the first six terms of the sequence of negative odd numbers starting from negative one.

In this question, we’re asked to write the first six terms of the sequence of negative odd numbers. We need to start from negative one. To do this, let’s start by recalling what we mean by a negative odd number. First, we recall an odd number is an integer which is not an integer multiple of two. Second, we recall a negative number is a real number which is less than zero. We’re told the first term of this sequence is negative one, so we can write the first term of our sequence. We then need to determine the second term.

First, the next term in this sequence is odd, so it must be an integer value. Second, we know that the second term in this sequence is negative, so it must be less than zero. And finally, it’s not allowed to be an integer multiple of two. Let’s find the terms of this sequence by starting with the negative integers starting at negative one. These are negative one, negative two, negative three, all the way up to negative six, where we’ll stop our sequence for now. We can find the sequence of negative odd numbers starting from negative one by removing the nonodd numbers from this list. To do this, we just need to find all of the nonodd numbers.

Remember, nonodd numbers are called even numbers. We can see that negative two is an even number because it’s two multiplied by negative one. Similarly, negative four is an even number and negative six is an even number because they’re integer multiples of two. However, negative three and negative five are odd numbers; they’re not integer multiples of two. And we know if we add or subtract two from an even number, we’ll have an even number. And if we add or subtract two from an odd number, we will have an odd number. This means we can generate the next negative odd number by subtracting two from the previous negative odd number.

In other words, we’ve just shown the sequence of negative odd numbers starting from negative one is an arithmetic sequence with common difference negative two. We can then use this to generate the first six terms of this sequence. Negative five minus two is negative seven. Negative seven minus two is negative nine. And negative nine minus two is negative 11. Therefore, we’ve shown the first six terms of the sequence of negative odd numbers starting from negative one is negative one, negative three, negative five, negative seven, negative nine, and negative 11.

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