Geometric sequence

Geometric sequence formula

The sum of the terms of all the given terms of a geometric sequence is called as a geometric series. Thus, the general form of a geometric sequence is,

a, ar, ar², ar³, ar⁴……

and that of a geometric series is,

a + ar + ar² + ar³ + ar⁴ +…..

The nth term of a geometric sequences with initial a and the ratio r is given by,

a_n = ar^n-1

Here, r → common ratio, n → total no. of terms in the series

Such a geometric sequences may follows the recursive relation in some cases,

a_n = ra_n-1 for every integer n>=1

Here, r → Common ratio, n → no. of terms in the series

For checking whether the given sequence is geometric or not, we have to simply check whether successive entries in the sequence all have the same ratio. For instance,

1, −2, 4, −8, 16, −32…

is a geometric sequence with r value −2.