Question

The sum of the first n terms of an arithmetic sequence is n/2(4n + 20).

a) Write down the expression for the sum of the first (n − 1) terms.
b) Find the first term and common difference of the above sequence.
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Answer 1

(a).

`S_(n) = (n)/(2) (4n + 20) \\ \\S _(n - 1) = ((n - 1))/(2) (4n - 4 + 20) \\ \\ S _(n - 1) = ((n - 1))/(2) (4n + 16) \\ \\S _(n - 1) = ((n - 1)(4n + 16))/(2) \\ \\ { \boxed{S _(n - 1) = {2 {n}^(2) + 6n - 8}}} \\`

(b).

from general equation:

`S _(n - 1) = ((n - 1))/(2) (4n + 16)`

first term is 4n

common difference:

`16 = \{(n - 1) - 1 \}d \\ 16 = (n - 2)d \\ d = (16)/(n - 2)`