Easy -1.2 This is a straightforward application of standard summation formulae requiring only algebraic manipulation (expanding to 3∑r² - 2∑r) and substitution of n=10 into given formulae. It's a routine Further Maths exercise with no problem-solving or insight required, though slightly above basic A-level due to the Further Pure context.
4 Using the formulae for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\), show that \(\sum _ { r = 1 } ^ { 10 } r ( 3 r - 2 ) = 1045\).
4 Using the formulae for $\sum _ { r = 1 } ^ { n } r$ and $\sum _ { r = 1 } ^ { n } r ^ { 2 }$, show that $\sum _ { r = 1 } ^ { 10 } r ( 3 r - 2 ) = 1045$.
\hfill \mbox{\textit{OCR Further Pure Core 1 2019 Q4 [3]}}