Solving the Polynomial Sequence: Finding First Two Terms of n^2+1

Question

For the series n2+1 n^2+1

Find the first two terms.

Video Solution

Solution Steps

00:05 Alright, let's find the first two elements in the sequence.
00:09 We'll start by substituting the position we want into the sequence formula. Let's solve it step by step.
00:15 Remember, always calculate exponents first to get the correct result.
00:21 Great job! That's the first element in our sequence.
00:25 Now, let's use the same steps to find the second element.
00:29 Again, substitute the position into the formula, and solve it carefully.
00:36 Make sure you tackle the exponents first here as well.
00:41 And there you have it! That's how we solve this question. Nice work!

Step-by-Step Solution

To solve this problem, we determine the terms of the series using the given formula n2+1 n^2 + 1 .

We'll evaluate this series for the first two positive integer values of n n .

  • For n=1 n = 1 , the term is 12+1=1+1=2 1^2 + 1 = 1 + 1 = 2 .
  • For n=2 n = 2 , the term is 22+1=4+1=5 2^2 + 1 = 4 + 1 = 5 .

Hence, the first two terms of the series are 2 and 5. Among the choices provided, the correct answer is 2,5.

Answer

2,5

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