Problem 61 - Algebra and Trigonometry

Question

Will help you prepare for the material covered in the first section of the next chapter. Evaluate \(j^{2}+1\) for all consecutive integers from 1 to 6 inclusive. Then find the sum of the six evaluations.

Step-by-Step Solution

Answer

The sum of the evaluations of the expression \(j^{2}+1\) for the integers from 1 to 6 is 97.

Step 1: Substitution for \(j\)

We substitute the integers 1, 2, 3, 4, 5, and 6 for \(j\) in the expression \(j^{2}+1\). This results in the following six expressions: \(1^{2}+1\), \(2^{2}+1\), \(3^{2}+1\), \(4^{2}+1\), \(5^{2}+1\), and \(6^{2}+1\).

Step 2: Evaluation of each expression

We evaluate each of the six expressions: \(1^{2}+1 = 2\), \(2^{2}+1 = 5\), \(3^{2}+1 = 10\), \(4^{2}+1 = 17\), \(5^{2}+1 = 26\), \(6^{2}+1 = 37\).

Step 3: Summation of the results

We add up the results from step 2: \(2 + 5 + 10 + 17 + 26 + 37 = 97\).