What is the sum of the first 6 terms of the arithmetic progression 1, 4, 7, ...?

What is the sum of the first 6 terms of the arithmetic progression 1, 4, 7, ...?

Step 1: Identify the first term of the arithmetic progression (AP). The first term (a) is 1.
Step 2: Identify the common difference of the AP. The common difference (d) is found by subtracting the first term from the second term: 4 - 1 = 3.
Step 3: Determine how many terms we want to sum. We want the sum of the first 6 terms (n = 6).
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_6 = 6/2 * (2*1 + (6-1)*3).
Step 6: Calculate 6/2, which equals 3.
Step 7: Calculate (6-1)*3, which equals 5*3 = 15.
Step 8: Calculate 2*1 + 15, which equals 2 + 15 = 17.
Step 9: Multiply 3 by 17 to find the sum: 3 * 17 = 51.
Step 10: The sum of the first 6 terms of the arithmetic progression is 51.

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