1.28: The sum of the first terms of an arithmetic series is An where

4PM1/2/June/2019 — Question 7 · 9 marks

The sum of the first n\displaystyle n terms of an arithmetic series is An where
A ln = ∑r=1n (4r⋆+5)\displaystyle {\mathit{l}}_{n}\,=\,\sum_{r=1}^{n}\,(4r^{\star}+5)
(a) For this arithmetic series, find
(i) the first term,
(ii) the common difference.
(2)
The sum of the first n\displaystyle n terms of a geometric series is Gn where
Gn =∑r=1n4(3)r−1\displaystyle =\sum_{r=1}^{n}4(3)^{r-1}
(b) For this geometric series, find
(i) the first term,
(ii) the common ratio.
(2)
(c) Find the value of n\displaystyle n for which A14 −6=\displaystyle - 6 = Gn
(5)