A sequence of numbers is in arithmetic progression. If the first term is 8 and t
Practice Questions
Q1
A sequence of numbers is in arithmetic progression. If the first term is 8 and the last term is 32, and there are 6 terms, 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 8 and the last term is 32, and there are 6 terms, what is the common difference?
Step 1: Identify the first term (a) of the arithmetic progression, which is given as 8.
Step 2: Identify the last term of the arithmetic progression, which is given as 32.
Step 3: Identify the number of terms (n) in the sequence, which is given as 6.
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: 32 = 8 + (6 - 1) * d.
Step 6: Simplify the equation: 32 = 8 + 5d.
Step 7: Subtract 8 from both sides: 32 - 8 = 5d, which simplifies to 24 = 5d.
Step 8: Divide both sides by 5 to find the common difference (d): d = 24 / 5.
Step 9: Calculate the value: d = 4.8.
Arithmetic Progression – A sequence of numbers in which the difference between consecutive terms is constant.
Formula for the Last Term – The last term of an arithmetic sequence can be calculated using the formula: a + (n-1)d, where 'a' is the first term, 'n' is the number of terms, and 'd' is the common difference.
