Answer the following below

Question

For each of the following arithmetic sequences,

(a) Write a non-recursive formula for the nth partial sum, S_n, of the given arithmetic sequence.

(b) Calculate S₂₅.

1. -18, -14, -10, -6, -2, ...
2. A_n=-4n+5 for n= 1, 2, 3, ...
3. A₁=2, A_n = A_n-1 +10 for n=2, 3, 4, ...

Answer 1

1) S₂₅ = (25/2)[2(-18) + 24(4)]

2) S₂₅ = (25/2)[2(1) + 24(-4)]

3) S₂₅ = (25/2)[2(2) + 24(10)]