First term defines the starting value. Common difference is added repeatedly to generate subsequent terms. Sequence continues infinitely. Arithmetic pattern maintains constant difference between consecutive terms. Values grow steadily and evenly with equal steps. Each term can be found by adding common difference to previous term.
An arithmetic progression has numbers arranged in a pattern where each term differs from the previous term by a fixed number. The first term defines the sequence start. Common difference remains constant throughout. Terms can be found using first term and common difference. Pattern helps find missing terms sum of terms or nth term position.
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This is the right formula for sum of n terms of an AP.
Let’s check why:
1) For an AP with first term a₁ and common difference d:
Last term (aₙ) = a₁ + (n-1)d
2) In an AP, sum of first and last term = sum of second and second last term =.
Hence, Sₙ = n/2(first term + last term)
3) Putting last term:
Sₙ = n/2[a₁ + {a₁ + (n-1)d}]
= n/2[2a₁ + (n-1)d]
4) This formula yields:
– When n = 1: S₁ = a₁
– When n = 2: S₂ = 2a₁ + d
– When n = 3: S₃ = 3a₁ + 3d
And so on.
Thus, Sₙ = n/2[2a₁ + (n-1)d] is the right formula.
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