Is the sequence with general term three 𝑛 plus 79, where 𝑛 is in the positive integers, finite or infinite?
So here we have a general term of three 𝑛 plus 79. Any sequence is created by plugging numbers into 𝑛. And the numbers we are plugging into 𝑛 are in the set of the positive integers. Now the normal set of integers are negatives, zero, and positives. And these are numbers excluding fractions. So if our set only includes the positive integers, then it will be one, two, three, four, five, six, and so on, all the way to infinity.
So if the numbers that we are plugging in go on forever, and we know that by the dot dot dot, then this set would be infinite, meaning it does not end. So if we’re plugging an infinite amount of numbers into our general term, then our sequence must be infinite. Therefore, the given sequence is infinite as the set of positive integers is infinite.