A sequence of numbers is in arithmetic progression. If the first term is 12 and
Practice Questions
Q1
A sequence of numbers is in arithmetic progression. If the first term is 12 and the last term is 48, and there are 8 terms in total, what is the common difference?
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Questions & Step-by-Step Solutions
A sequence of numbers is in arithmetic progression. If the first term is 12 and the last term is 48, and there are 8 terms in total, what is the common difference?
Step 1: Identify the first term (a) of the arithmetic progression, which is given as 12.
Step 2: Identify the last term of the arithmetic progression, which is given as 48.
Step 3: Identify the total number of terms (n) in the sequence, which is given as 8.
Step 4: Use the formula for the last 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 + (8 - 1) * d.
Step 6: Simplify the equation: 48 = 12 + 7d.
Step 7: Subtract 12 from both sides: 48 - 12 = 7d, which simplifies to 36 = 7d.
Step 8: Divide both sides by 7 to find the common difference: d = 36 / 7.
Step 9: Calculate the value: d = 4.
Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
Nth Term Formula – The formula for the nth term of an arithmetic sequence is given by a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.
