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UPSC NDA I 2025 Mathematics Paper

Question : 120 of 120

Marks: +1, -0

8^{2},9^{2},10^{2},...,15^{2}

Solution:

Concept:

The arithmetic mean is the sum of numbers divided by the count. Use the formula for sum of squares:

\frac{n(n+1)(2n+1)}{6}

Explanation:

Number of terms from

8^2

15^2

15-8+1 = 8

Sum of squares up to

15

S_{15} = \frac{15\cdot16\cdot31}{6} = 1240

Sum of squares up to

7

S_7 = \frac{7\cdot8\cdot15}{6} = 140

Sum of required squares:

1240 - 140 = 1100

Arithmetic mean:

\frac{1100}{8} = 137.5

Answer:

The arithmetic mean is

137.5

. Hence, the correct option is C.

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