What is the sum of the first 5 terms of the arithmetic sequence 2, 5, 8, ...?
Practice Questions
Q1
What is the sum of the first 5 terms of the arithmetic sequence 2, 5, 8, ...?
30
25
20
15
Questions & Step-by-Step Solutions
What is the sum of the first 5 terms of the arithmetic sequence 2, 5, 8, ...?
Step 1: Identify the first term of the sequence. The first term (a) is 2.
Step 2: Identify the common difference of the sequence. The common difference (d) is found by subtracting the first term from the second term: 5 - 2 = 3.
Step 3: Determine how many terms you want to sum. We want to sum the first 5 terms (n = 5).
Step 4: Use the formula for the sum of the first n terms of an arithmetic sequence: Sum = n/2 * (2a + (n-1)d).
Step 5: Plug in the values into the formula: Sum = 5/2 * (2*2 + (5-1)*3).
Step 6: Calculate the expression inside the parentheses: 2*2 = 4 and (5-1)*3 = 12, so we have 4 + 12 = 16.
Step 7: Now calculate the sum: Sum = 5/2 * 16.
Step 8: Multiply: 5/2 * 16 = 5 * 8 = 40.
Step 9: The sum of the first 5 terms of the sequence is 40.
