Question:
The 10th term of an arithmetic progression is 35 and the 20th term is 65. What is the first term?
The 10th term of an arithmetic progression is 35 and the 20th term is 65. What is the first term?
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Use the formula \(a_n = a + (n-1)d\) for arithmetic progression problems to find \(a\) and \(d\) by setting up simultaneous equations.
Updated On: May 27, 2025
- 10
- 8
- 5
- 15
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The Correct Option is B
Solution and Explanation
Step 1: Let the first term be \(a\) and common difference be \(d\).
The \(n\)th term of A.P. is given by: \[ a_n = a + (n-1)d. \]
Step 2: Given, \[ a_{10} = a + 9d = 35, \] \[ a_{20} = a + 19d = 65. \]
Step 3: Subtracting the first equation from the second: \[ (a + 19d) - (a + 9d) = 65 - 35 \implies 10d = 30 \implies d = 3. \]
Step 4: Substitute \(d = 3\) into \(a + 9d = 35\): \[ a + 9 \times 3 = 35 \implies a + 27 = 35 \implies a = 8. \]
Step 5: Check options, \(a=8\) is option (B).
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