A Recurrence from Sums

★ 8/10Arithmetic Progression Recursion sequences

Problem

Let $S_n$ be the partial sums of a sequence $\{a_n\}$ with $a_1 = 1$ , $a_2 = 6$ , $a_3 = 11$ , and

(5n - 8)S_{n+1} - (5n + 2)S_n = An + B, \qquad n = 1, 2, \ldots,

where $A, B$ are constants.

1. Find $A$ and $B$ . 2. Find a formula for $a_n$ .

Answer

Solution

Difficulty	8/10
Topics	Arithmetic Progression, Recursion, sequences

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.