1.16: Show that (b) Hence, or otherwise, evaluate Given that (c) find the value of

4PM1/1/June/2024 — Question 3 · 8 marks

(a) Show that r=1n(5r3)=n2(5n1)\displaystyle \sum_{r=1}^n (5r - 3) = \frac{n}{2}(5n - 1)
(3)
(b) Hence, or otherwise, evaluate r=3160(5r3)\displaystyle \sum_{r=31}^{60} (5r - 3)
(2)
Given that r=1n(5r3)=3783\displaystyle \sum_{r=1}^n (5r - 3) = 3783
(c) find the value of n\displaystyle n
(3)