Question Video: Finding the Terms of a Sequence of Even Numbers under a Certain Condition Then Finding Its General Term Mathematics

Video Transcript

Find the sequence and its general term of all the even numbers greater than 62.

We know that a sequence is a set of numbers that follow a rule or pattern. In this question, our sequence contains the even numbers greater than 62. This means that our first number is 64. The next four numbers are 66, 68, 70, and 72. The sequence of even numbers greater than 62 is 64, 66, 68, 70, 72, and so on.

We are also asked to find the general term of this sequence. We know that the general term, or 𝑛th term, of an arithmetic sequence can be found using the formula 𝑎 sub 𝑛 is equal to 𝑎 sub one plus 𝑛 minus one multiplied by 𝑑, where 𝑎 sub one is the first term in the sequence and 𝑑 is the common difference. We know that any sequence with a common difference between consecutive terms is an arithmetic sequence.

In our sequence, the common difference is two, as each even number is two larger than the previous even number. The first term of our sequence, 𝑎 sub one, is equal to 64. Substituting these values into our formula, we have 𝑎 sub 𝑛 is equal to 64 plus two multiplied by 𝑛 minus one. Distributing the parentheses gives us two 𝑛 minus two. 𝑎 sub 𝑛 is therefore equal to 64 plus two 𝑛 minus two. And collecting like terms, this simplifies to two 𝑛 plus 62. The general term of all the even numbers greater than 62 is two 𝑛 plus 62.