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

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

Options:

  1. 15
  2. 30
  3. 20
  4. 25

Correct Answer: 20

Solution: 

The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d). For n = 5, S_5 = 5/2 * (2*2 + 4*3) = 5/2 * (4 + 12) = 5/2 * 16 = 40/2 = 20.

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

Practice Questions

Q1
What is the sum of the first 5 terms of the arithmetic progression 2, 5, 8, ...?
  1. 15
  2. 30
  3. 20
  4. 25

Questions & Step-by-Step Solutions

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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