-- you have 2 rows for sector 'A', month 1
-- what do you want to do with them?
-- It's not clear from your "Required Output", which is incorrect
-- see row 3.
SELECT
[IncreaseDecreaseAmount] = ISNULL(cr.Amount-lr.Amount,cr.Amount),
cr.Amount,
cr.Monthno,
cr.sector
FROM @t cr
LEFT JOIN (
SELECT Sector, monthno, [Amount] = SUM([Amount])
FROM @t
GROUP BY Sector, monthno
) lr ON lr.Sector = cr.Sector AND lr.monthno+1 = cr.monthno
ORDER BY cr.sector, cr.Monthno
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden