To find the sum of an AP terms multiply the number of terms with the average of first and last terms. First get the last term by adding common difference (n-1) times to first term and then apply the formula.
In this chapter you will learn about sequences where consecutive terms have a constant difference called arithmetic progressions. The chapter covers finding terms using nth term formula. You will study methods to find sum of n terms and solving word problems based on real-life applications of APs.
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Given Sₙ = n(n+1)
To calculate mᵗʰ term:
aₘ = Sₘ – S(m-1)
When n = m:
Sₘ = m(m+1)
When n = m-1:
S(m-1) = (m-1)(m)
Thus:
aₘ = m(m+1) – (m-1)(m)
= m² + m – m² + m
= 2m
Adding 1 to obtain S₁ = 1:
aₘ = 2m + 1
To confirm:
– When m = 1: a₁ = 3
– When m = 2: a₂ = 5
– When m = 3: a₃ = 7
This is an AP with d = 2
Also, sum of n terms = n(n+1) is fulfilled
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