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A certain arithmetic progression has a first term of 12 and a last term of 48. I

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Question: A certain arithmetic progression has a first term of 12 and a last term of 48. If there are 10 terms in total, what is the common difference?

Options:

  1. 4
  2. 3
  3. 5
  4. 6

Correct Answer: 4

Solution: 

The common difference d can be calculated using the formula for the nth term: a + (n-1)d = last term. Here, 12 + 9d = 48, solving gives d = 4.

A certain arithmetic progression has a first term of 12 and a last term of 48. I

Practice Questions

Q1
A certain arithmetic progression has a first term of 12 and a last term of 48. If there are 10 terms in total, what is the common difference?
  1. 4
  2. 3
  3. 5
  4. 6

Questions & Step-by-Step Solutions

A certain arithmetic progression has a first term of 12 and a last term of 48. If there are 10 terms in total, what is the common difference?
  • Step 1: Identify the first term of the arithmetic progression, which is 12.
  • Step 2: Identify the last term of the arithmetic progression, which is 48.
  • Step 3: Identify the total number of terms, which is 10.
  • Step 4: Use the formula for the nth term of an arithmetic progression: last term = first term + (number of terms - 1) * common difference.
  • Step 5: Substitute the known values into the formula: 48 = 12 + (10 - 1) * d.
  • Step 6: Simplify the equation: 48 = 12 + 9d.
  • Step 7: Subtract 12 from both sides: 48 - 12 = 9d, which gives 36 = 9d.
  • Step 8: Divide both sides by 9 to find d: d = 36 / 9.
  • Step 9: Calculate the value of d: d = 4.
  • Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
  • Nth Term Formula – The nth term of an arithmetic progression can be calculated using the formula: a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.
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