Find the first five terms and the general term, in terms of 𝑛, of the sequence of all the odd numbers greater than 21.
The odd numbers are all the numbers not divisible by two. They end in one, three, five, seven, and nine. The first odd number that is greater than 21 is 23. This is followed by 25, 27, 29, and 31. The first five terms of the sequence of all the odd numbers greater than 21 are 23, 25, 27, 29, and 31. The general term 𝑎 𝑛 of any arithmetic sequence is given by 𝑎 plus 𝑛 minus one multiplied by 𝑑, where 𝑎 is the first term in the sequence and 𝑑 is the common difference. 𝑎 is also sometimes denoted by 𝑎 sub one.
The first term in our sequence is 23. As each odd number is two greater than the previous odd number, the common difference 𝑑 is equal to two. 𝑎 sub 𝑛 is therefore equal to 23 plus 𝑛 minus one multiplied by two. We can distribute the parentheses or expand the brackets by multiplying two by 𝑛 and two by negative one. This gives us two 𝑛 minus two. Collecting our like terms, 23 and negative two, gives us 21. The general term, in terms of 𝑛, is therefore equal to two 𝑛 plus 21.