Find the S₃ of the sequence: aₙ = -3 + 2n²

To find the sum \( S_3 \) of the sequence \( a_n = -3 + 2n^2 \), we need to calculate the first three terms of the sequence and then sum them up.

### Step 1: Find the first three terms of the sequence.

1. \( a_1 = -3 + 2(1)^2 = -3 + 2(1) = -3 + 2 = -1 \)
2. \( a_2 = -3 + 2(2)^2 = -3 + 2(4) = -3 + 8 = 5 \)
3. \( a_3 = -3 + 2(3)^2 = -3 + 2(9) = -3 + 18 = 15 \)

### Step 2: Sum the first three terms.

\( S_3 = a_1 + a_2 + a_3 \)

\( S_3 = -1 + 5 + 15 = 19 \)

So, the sum \( S_3 \) of the first three terms is **19**.

Would you like further details or have any questions about this solution?

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Here are 5 related questions you might find interesting:

1. What is the sum \( S_4 \) of the first four terms of the sequence \( a_n = -3 + 2n^2 \)?
2. What is the general formula for the sum \( S_n \) of the first \( n \) terms of the sequence?
3. How does the sequence change if the formula is modified to \( a_n = -3 + 2n^3 \)?
4. What is the value of the 10th term \( a_{10} \) of the sequence?
5. How does the sequence behave as \( n \) becomes very large (as \( n \to \infty \))?

**Tip:** When dealing with sequences, identifying a pattern in the first few terms can often help predict future terms or sum formulas.

Discover how to find the sum S₃ of the sequence aₙ = -3 + 2n² with a step-by-step solution. This problem involves calculating the first three terms of a quadratic sequence and summing them up using the arithmetic series sum formula. Suitable for advanced high school students.

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