the rth term of an arithmetic sequence is (2r-5), show the sum of (n on top of letter, r=1 on bottom) (2r-5)=n(n-4)

Question

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Answer 1

for r = 1,2,...,n you want ∑(2r-5) = 2(∑r) - 5n = 2[n(n+1)/2] - 5n = n(n+1) - 5n = n² - 4n = n(n-4).