Question

Which of the following represents a geometric sequence? I 1/4, 1/4, 1/4, 1/4 II 1/4, 1/5, 1/6 III 1/4, 1, -4, 1/6 IV 1/4, -4, 1/4, -4

Answer 1

I'm pretty sure it would be none of these because1/4*5=1 and 1/4 then it would be 6 and 1/4 then it would be 31 and 1/4

Answer 2

option I is a geometric sequence

Explanation:

I 1/4, 1/4, 1/4, 1/4

II 1/4, 1/5, 1/6

III 1/4, 1, -4, 1/6

IV 1/4, -4, 1/4, -4

For any geometric sequence there should be a common ratio

To find common ratio we divide consecutive terms

lets check option I

I 1/4, 1/4, 1/4, 1/4

When we divide 1/4 by 1/4 we will get 1

Same 1 for other two terms, so common ratio is 1

Hence first option is a geometric sequence