What is the sum of the first 5 terms of the arithmetic progression 2, 5, 8, ...?

What is the sum of the first 5 terms of the arithmetic progression 2, 5, 8, ...?

Step 1: Identify the first term of the arithmetic progression (AP). The first term (a) is 2.
Step 2: Identify the common difference (d) of the AP. The common difference 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 progression: S_n = n/2 * (2a + (n-1)d).
Step 5: Substitute the values into the formula: S_5 = 5/2 * (2*2 + (5-1)*3).
Step 6: Calculate the expression inside the parentheses: 2*2 = 4 and (5-1)*3 = 4*3 = 12, so 4 + 12 = 16.
Step 7: Now substitute back into the formula: S_5 = 5/2 * 16.
Step 8: Multiply: 5/2 * 16 = 80/2 = 40.
Step 9: Therefore, the sum of the first 5 terms is 40.

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