Determine if the series is convergent or divergent -5+25-125+

a) convergent
b) divergent

b)Divergent

Step-by-step explanation:

Given is a series

-5+25-125+....

We find that this is following a pattern such that each term is multiplied by -5 to get the next term

In other words, this series is a geometric series with common ratio r =-5 and I term a=-5

Since sum of n terms of geometric series =

Since |r|=|-5|>1, we find that this sum tends to infinity or -infinity as n tends to infinity

In other words, the series diverges

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2