Sequences

Question 1

Formula for nth term of an arithmetic sequence

Answer 1

Un= a +(n - 1)d

Question 2

The sum of the first n terms of an arithmetic series

Answer 2

Sn= n/2( 2a +(n - 1)d)
or
Sn=n/2 (a+l)

Question 3

Formula for geometric sequence

Answer 3

Un= ar^n-1

Question 4

Sum of the first n terms of a geometric series

Answer 4

Sn= a(1-r^n)/(1- r)
or
Sn= a(r^n-1)/(r - 1)

Question 5

Sum to infinity

Answer 5

When terms are getting larger it’s a divergent series, when they are smaller as n tends to infinity, the sum gets closer to a finite number making it convergent series. It is convergent if and only if |r|< 1

Question 6

The sum to infinity of a convergent series

Answer 6

S ∞= a/(1 - r)

Question 7

Recurrence relations

Answer 7

A sequence is periodic if the terms repeat in a cycle. This means there is an integer k such that U(n+k) = Un for all n. The value of k is called the order