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In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what
In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?
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Q1
In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?
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Let the common difference be d. From the equations 4 + 5d = 24, solving gives d = 4.
Questions & Step-by-step Solutions
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Q
Q: In an arithmetic progression, if the 1st term is 4 and the 6th term is 24, what is the common difference?
Solution:
Let the common difference be d. From the equations 4 + 5d = 24, solving gives d = 4.
Steps: 8
Show Steps
Step 1: Identify the first term of the arithmetic progression, which is given as 4.
Step 2: Identify the sixth term of the arithmetic progression, which is given as 24.
Step 3: Recall the formula for the nth term of an arithmetic progression: nth term = first term + (n-1) * common difference.
Step 4: For the sixth term (n=6), the formula becomes: 6th term = 4 + (6-1) * d.
Step 5: Substitute the known values into the equation: 24 = 4 + 5d.
Step 6: Simplify the equation: 24 - 4 = 5d, which gives 20 = 5d.
Step 7: Solve for d by dividing both sides by 5: d = 20 / 5.
Step 8: Calculate the value of d: d = 4.
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