# Question Video: Finding the Terms of a Sequence Given the πth Term Mathematics

Find the first five terms of the sequence whose πth term is given by π_π = 5πΒ² + πΒ³.

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### Video Transcript

Find the first five terms of the sequence, whose πth term is given by π π equals five π squared plus π cubed.

Remember, the πth 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 π be equal to 10. And similarly, if we wanted to find the 25th term in the sequence, we would let π be equal to 25. In this question, weβre looking to find the first five terms of the sequence. It follows then that to find the first term, weβll let π be equal to one. To find the second term, weβll let π be equal to two. For the third term, weβll let π be equal to three. And then, weβll let π be equal to four to find the fourth term and π be equal to five to find the fifth term.

All thatβs left is to substitute each of these values of π into our πth term rule. Well, the πth term rule is five π squared plus π 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 πth is given by π π equals five π squared plus π cubed. They are six, 28, 72, 144, and 250.