Sequences and Series — Formula Sheet

a1 = 1, a2 = 1, a_n = a_(n-1) + a_(n-2) for n >= 3

a_n = a + (n-1)d

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

d = a_(n+1) - a_n

If a, b, c are in A.P., then a + c = 2b

pth term from the end = (n-p+1)th term from the beginning

A = (a+b)/2

d = (b-a)/(n+1)

A_k = a + kd, k = 1,2,...,n

Sum of n arithmetic means between a and b = n(a+b)/2

If a, b, c are in A.P., then a + c = 2b.

If a, b, c are in G.P., then ac = b^2.