A geometric sequence
is a sequence of numbers each of which, after the first, is obtained by multiplying the preceding number a constant number called the common rate.
3, 6, 12, 24, 48,... is a geometric sequence because each term is obtained by multiplying the preceding number by 2.
To solve exercises using geometric sequences you need the following formula:
The nth term: an=a1·rn-1
a1 = the first term of the sequence
= common rate
n = number of terms
an = nth term
Given 27, -9, 3, -1, ... Find an and a8
Given a geometric sequence with a2
=-10 and a5
=-80. Find an
, so we need to find a1
To find it we use the next system of equations:
solving by substitution:
That is an=-5·2n-1
8 term of the geometric sequence where
the first terms are: -1,2,-4,8,...