Sequences and Series Formulas

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)

Arithmetic Sequence

t_n = t₁ +(n-1)d

Series(sum) = S_n, = n(t₁ + t_n)/2

Geometric Sequence

t_n = t₁. r^(n-1)

Series: S_n = [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

n=[(l−a)/d]+1

=[(72−8)/4]+1

=[64/4]+1

=16+1

=17

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