Sequences

Linear Recurrence Relation

T_n+1=bT_n+c , T₁= a

Arithmetic Recursive Equation

T_n+1 = T_n+d , T₁ = a

a = first term

d = common difference

Tn = term value

Arithmetic Explicit Rule for the nth term

T_n = a + (n - 1)d

Tn = term value

a = first term

n = term position 

d = common difference

Geometric Recursive Equation

T_n+1 = T_n x r , T₁ = a

a = first term

Tn = term value

r = common ratio

n = term position

Geometric Explicit rule for the nth term

T_n = a x r^n-1

a = first term

r = common ratio

tn = term value

n = term position

Common Difference:

d = t2 - t1

Common Ratio

r = t_n+1/t_n

or

r = t₂ / t₁

or

r = any term / previous term