The sum of the 4th and 8th terms of an AP is 24, and the sum of the 6th and 10th terms is 44. What is the first term of the AP?
Answer and explanation
Correct answer: A. -13
- Step 1: a_4 + a_8 = (a + 3d) + (a + 7d) = 2a + 10d = 24 => a + 5d = 12.
- Step 2: a_6 + a_10 = (a + 5d) + (a + 9d) = 2a + 14d = 44 => a + 7d = 22.
- Step 3: Subtract: (a + 7d) - (a + 5d) = 2d = 10 => d = 5.
- Step 4: a = 12 - 5(5) = 12 - 25 = -13.
Why not the others: -15, -11 and -9 do not fit.
Practise more Arithmetic progressions.
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