1.30: Arithmetic Series and Term Relations

4PM1/1/January/2019 — Question 2 · 8 marks

The sum of the first n\displaystyle n terms of an arithmetic series is Sn\displaystyle S_n.
Given that
Sn=∑r=1n(4r+1),S_n=\sum_{r=1}^{n}(4r+1),
(a) show that
Sn=n(3+2n).S_n=n(3+2n).
(4)
The r\displaystyle rth term of this arithmetic series is tr\displaystyle t_r.
Given that
Sn+3=Sn+3t15,S_{n+3}=S_n+3t_{15},
(b) find the value of n\displaystyle n.
(4)