For understanding and using Sequence and Series formulas, we should know what Sequence and series are.
What is the Sequence?
An ordered list of numbers which is defined for positive integers. Example: (1,2,3,4)
What is a series?
It is the sum of the terms of the sequence and not just the list. Example ( 1+ 2+3+4 =10)
tn = t1 +(n-1)d
Series(sum) = Sn, = n(t1 + tn)/2
tn = t1. r(n-1)
Series: Sn = [t1 (1 – rn)] / [1-r]
S = t1 / 1 – r
Examples of Sequence and Series Formulas
Let’s use the sequence and series formulas now in an example.
Question 1: Find the number of terms in the following series
8, 12, 16, . . .72
Solution: a(first term of the series) = 8
l(last term of the series) = 72
d(difference between second and first term) = 12 – 8 = 4