Video: Finding the Terms of a Sequence Given the 𝑛th Term

Find the first five terms of the sequence whose 𝑛th term is given by π‘Ž_𝑛 = 5𝑛² + 𝑛³.

01:35

Video Transcript

Find the first five terms of the sequence, whose 𝑛th term is given by π‘Ž 𝑛 equals five 𝑛 squared plus 𝑛 cubed.

Remember, the 𝑛th term is a rule that allows us to find any term in the sequence. For example, if we wanted to find the 10th term in a sequence, we would let 𝑛 be equal to 10. And similarly, if we wanted to find the 25th term in the sequence, we would let 𝑛 be equal to 25. In this question, we’re looking to find the first five terms of the sequence. It follows then that to find the first term, we’ll let 𝑛 be equal to one. To find the second term, we’ll let 𝑛 be equal to two. For the third term, we’ll let 𝑛 be equal to three. And then, we’ll let 𝑛 be equal to four to find the fourth term and 𝑛 be equal to five to find the fifth term.

All that’s left is to substitute each of these values of 𝑛 into our 𝑛th term rule. Well, the 𝑛th term rule is five 𝑛 squared plus 𝑛 cubed. So the first term is given by five times one squared plus one cubed, which is equal to six. Then, the second term is given by five times two squared plus two cubed, which is 28. The third term is five times three squared plus three cubed, which is equal to 72. Then, the fourth term is five times four squared plus four cubed, which is 144. And the fifth is five times five squared plus five cubed, which is 250.

And so, we found the first five terms of the sequence whose 𝑛th is given by π‘Ž 𝑛 equals five 𝑛 squared plus 𝑛 cubed. They are six, 28, 72, 144, and 250.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.