Multiple choice general knowledge math & puzzles

The sum of 5 numbers in A.P is 30 and the sum of their squares is 220. Then the third term is

  1. 8

  2. 6

  3. 9

  4. 10
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B Correct answer
Explanation

Let the 5 numbers in AP be a-2d, a-d, a, a+d, a+2d. Their sum is 5a = 30, giving a = 6. The third term (middle term) is a = 6. Verifying with sum of squares: (a-2d)² + (a-d)² + a² + (a+d)² + (a+2d)² = 5a² + 10d² = 180 + 10d² = 220, so d² = 4. The third term remains 6 regardless of d.

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