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If the first term of an arithmetic progression is 8 and the last term is 50, wit

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Question: If the first term of an arithmetic progression is 8 and the last term is 50, with a total of 10 terms, what is the common difference? (2023)

Options:

  1. 4
  2. 5
  3. 6
  4. 7

Correct Answer: 5

Exam Year: 2023

Solution: 

Using the formula for the nth term, we have 50 = 8 + (10-1)d. Solving for d gives us d = 5.

If the first term of an arithmetic progression is 8 and the last term is 50, wit

Practice Questions

Q1
If the first term of an arithmetic progression is 8 and the last term is 50, with a total of 10 terms, what is the common difference? (2023)
  1. 4
  2. 5
  3. 6
  4. 7

Questions & Step-by-Step Solutions

If the first term of an arithmetic progression is 8 and the last term is 50, with a total of 10 terms, what is the common difference? (2023)
  • Step 1: Identify the first term of the arithmetic progression (AP), which is given as 8.
  • Step 2: Identify the last term of the AP, which is given as 50.
  • Step 3: Identify the total number of terms in the AP, which is given as 10.
  • Step 4: Use the formula for the nth term of an AP: nth term = first term + (n-1) * common difference.
  • Step 5: Substitute the known values into the formula: 50 = 8 + (10-1)d.
  • Step 6: Simplify the equation: 50 = 8 + 9d.
  • Step 7: Subtract 8 from both sides: 50 - 8 = 9d, which simplifies to 42 = 9d.
  • Step 8: Divide both sides by 9 to solve for d: d = 42 / 9.
  • Step 9: Simplify the fraction: d = 4.67 (approximately) or d = 5 when rounded.
  • 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 = 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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