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

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

Options:

  1. 60
  2. 45
  3. 30
  4. 36

Correct Answer: 45

Solution: 

The first term a = 1, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d). For n = 6, S_6 = 6/2 * (2*1 + 5*3) = 3 * (2 + 15) = 3 * 17 = 51.

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

Practice Questions

Q1
What is the sum of the first 6 terms of the arithmetic progression 1, 4, 7, ...?
  1. 60
  2. 45
  3. 30
  4. 36

Questions & Step-by-Step Solutions

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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