UPSC NDA I 2025 Mathematics Paper

Given,
The sequence is 82,92,102,...,152
Number of terms, n=15−8+1=8
The sum of the first m squares is

m

∑

k=1

k2=‌

m(m+1)(2m+1)

6

Sum up to 152:
S15=‌

15×16×31

6

=1240
Sum up to 72:
S7=‌

7×8×15

6

=140
Sum of the required terms:
S=S15−S7=1240−140=1100
The arithmetic mean is,
‌ Mean ‌=‌

S

n

=‌

1100

8

=137.5
∴ The arithmetic mean is 137.5 .