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?
Practice Questions
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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?
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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.
Questions & Step-by-step Solutions
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Q
Q: 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?
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.
Steps: 9
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.
