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Alternating or mixed sums of squares and cubes

This type of question, asked 5 times: 31 Jan 2023, 6 Apr 2023, 13 Apr 2023, 4 Apr 2025, 6 Apr 2026 S1. All 5 questions below, oldest first.

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  1. Question 1

    31 Jan 2023

    180
    The sum 12−2⋅32+3⋅52−4⋅72+5⋅92−⋯+15⋅2921^{2}- 2 \cdot3^{2}+ 3 \cdot5^{2}- 4 \cdot7^{2}+ 5 \cdot9^{2}- \cdots + 15 \cdot29^{2} is

  2. Question 2

    6 Apr 2023

    169
    If gcd(m,n)=1gcd(m,n) = 1 and 12−22+32−42+1^{2}-2^{2}+3^{2}-4^{2}+ +(2021)2−(2022)2+(2023)2=1012m2n+ (2021)^{2}- (2022)^{2}+ (2023)^{2}= 1012m^{2}n, then m2−n2m^{2}-n^{2} is equal to

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  3. Question 3

    13 Apr 2023

    85
    The sum to 20 terms of the series 2.22−32+2.42−52+2.62−2.2^{2}-3^{2}+2.4^{2}-5^{2}+2.6^{2}- is equal to

  4. Question 4

    4 Apr 2025

    61
    1+3+52+7+92+…1 + 3 +5^{2}+ 7 +9^{2}+ \ldots upto 40 terms is equal to.

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  5. Question 5

    6 Apr 2026 S1

    55
    The value of 13−23+33−….+1531^{3}-2^{3}+3^{3}- \ldots. +15^{3} is:

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