An arithmetic sequence adds the same amount at every step.
WHAT HAPPENS IF…What is the sum of 1 through 6?
Interactive exploration
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Connect the picture to the ideaan=a1+(n−1)d,Sn=2n(a1+an)
After n−1 steps from the first term, the accumulated change is (n−1)d. Pair the first and last terms, then the second and next-to-last: every pair has the same sum a₁+aₙ. This gives the finite-sum formula, including odd n.
A detail that matters
The nth term uses n−1 increments from the first term.