Question

find the sum of 2^2+5^2+8^2+...............to 15 terms

Answer 1

$\displaystyle2^2+5^2+8^2+\dots +44^2\\\\(3\cdot1-1)^2+(3\cdot2-1)^2+(3\cdot3-1)^2+\dots +(3\cdot15-1)^2\\\\\sum_{n=1}^{15}\left ((3n-1)^2\right)\\\\\sum_{n=1}^{15}\left (9n^2-6n+1\right)\\\\9\sum_{n=1}^{15}n^2-6\sum_{n=1}^{15}n+\sum_{n=1}^{15}1\\\\\\9\cdot\dfrac{15\cdot16\cdot31}{6}-6\cdot\dfrac{15\cdot16}{2}+15\\\\11160-720+15\\\\\mathbf{10455}$