Question

True or False:

Answer 1

we can check if a given sequence is geometric or not by checking the terms present in it ,

Let us find ratio of each term with it's previous term

if that ratio comes out same for every two consecutive terms then it is a geometric sequence , otherwise it is not geometric sequence .

Let us work on first one : given is : -1,1,-1,1.............

second term/ first term = 1/-1 = -1

third term/ second term = -1/1 = -1

fourth term / third term = 1/-1 = -1

fifth term/ fourth term = -1/1 = -1

because that ratio is same so it is a geometric sequence .

* let us now work with second sequence .

eE

second term/ first term = -6/-2 = 3

third term/ second term = -18/ -6 = 3

fourth term / third term = -54 / -18 = 3

hence this is also geometric sequence .

Answer : both are geometric sequence .