Progressions — Formula Sheet

a, a + d, a + 2d, a + 3d, ...

a2 - a1 = a3 - a2 = ... = an - an-1 = d

d = a(k+1) - ak where k ∈ N; k ≥ 1

an = a + (n - 1)d

Sn = n/2 [2a + (n - 1)d]

a, ar, ar^2, ar^3, ...

a2/a1 = a3/a2 = ... = an/a(n-1) = r (r ≠ 1)

a_n = ar^(n-1)

a ≠ 0, r ≠ 0, r ≠ 1

Salary AP: 8000, 8500, 9000, 9500, 10000, ...

Money-box AP: 1000, 1500, 2000, 2500, ...

Interest AP: 80, 160, 240, ...

nth term of AP

a(n) = a + (n - 1)d.

The nth term of an AP with first term a and common difference d is a_n = a + (n - 1)d.

The sum of first n terms of an AP is S_n = n/2 [2a + (n - 1)d] or S_n = n/2 (a + l), where l is the last term.

The nth term of an AP is the difference of two consecutive partial sums: a_n = S_n - S_(n-1).