For Exercises 45–50, write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

Verified step by step guidance

1. Identify the sequence: The given expression is a summation of the form \( \sum_{i=1}^{100} 4i \), which represents an arithmetic sequence where each term is \( 4i \).
2. Write out the first three terms: Substitute \( i = 1, 2, 3 \) into \( 4i \) to get the first three terms: \( 4 \times 1, 4 \times 2, 4 \times 3 \).
3. Determine the last term: Substitute \( i = 100 \) into \( 4i \) to find the last term: \( 4 \times 100 \).
4. Use the formula for the sum of an arithmetic sequence: The sum \( S_n \) of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2} (a_1 + a_n) \), where \( a_1 \) is the first term and \( a_n \) is the last term.
5. Substitute the known values into the formula: Use \( n = 100 \), \( a_1 = 4 \times 1 \), and \( a_n = 4 \times 100 \) to find the sum.