1.6.3—Progression formulae

Use uₙ=a+(n−1)d for an arithmetic progression and uₙ=arⁿ⁻¹ for a geometric progression. Their finite sums follow from adding terms or multiplying by the common ratio.

Identify a,d or r from the information given, keep n as the term number, and check whether a sum is finite or infinite before choosing Sₙ or S∞.

For 5,8,11,…, uₙ=3n+2 and Sₙ=n(3n+7)/2; the first term is included once, not n times.

The nth term and nth partial sum are different quantities: Sₙ is not obtained by substituting n into uₙ.