Sequences and Series

used to find any term (nth term) of the arithmetic sequence, a1, a2, a3, ..., an,.... using its first term (a) and the common difference (d). This formula gives the nth term formula of an arithmetic sequence.

a formula that defines any term of a sequence in terms of its preceding term(s).

-an ordered set of numbers that have a common difference between each consecutive term

-an=a1+(n−1)d
-Sn= n/2[2a+(n-1)d]

-the sum of the terms in an arithmetic sequence with a definite number of terms.
-(1st term+last term)(total no.of terms/2)

-sum of values/no.of values

Average x n (position of term)

an ordered set of numbers that progresses by multiplying or dividing each term by a common ratio

the sum of the terms in a geometric sequence

the sum of an infinite geometric sequence

d= an/an-1

r= u3/u2

FV=PV (1+r/100k)^kn

yearly: 1
half-yearly (or semianually): 6
monthly: 12
Quaterly: 4

1. Find the r using the first and last term

2. substitute to find the terms [u1r^n-1=Un]

solve inequality based on the given value
eg. u1r^n-1<200

1. Identify the position of the last term

2. Find n [an=a+(n-1)d

Substitute the term with Un or an