If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?
Practice Questions
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Q1
If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?
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Let the first term be a and the common difference be d. From the equations a + 5d = 30 and a + 8d = 45, we can find d = 5.
Questions & Step-by-step Solutions
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Q
Q: If the 6th term of an arithmetic progression is 30 and the 9th term is 45, what is the common difference?
Solution: Let the first term be a and the common difference be d. From the equations a + 5d = 30 and a + 8d = 45, we can find d = 5.
Steps: 8
Step 1: Understand that in an arithmetic progression (AP), each term is found by adding a common difference (d) to the previous term.
Step 2: Identify the formula for the nth term of an AP, which is given by: nth term = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
Step 3: For the 6th term, set up the equation: a + 5d = 30.
Step 4: For the 9th term, set up the equation: a + 8d = 45.
Step 5: Now you have two equations: a + 5d = 30 and a + 8d = 45.
Step 6: To eliminate 'a', subtract the first equation from the second: (a + 8d) - (a + 5d) = 45 - 30.
Step 7: Simplify the equation: 3d = 15.
Step 8: Solve for d by dividing both sides by 3: d = 15 / 3 = 5.
