Question

While sorting some buttons, Erica put 35 buttons in the first box, 105 buttons in the second box, 315 buttons in the third box, and 945 buttons in the fourth box. What kind of sequence is this Both Arithmetic Neither Geometric

Answer 1

We conclude that 35, 105, 315, 945,... is a geometric sequence.

Explanation:

Given that Erica put 35 buttons in the first box, 105 buttons in the second box, 315 buttons in the third box, and 945 buttons in the fourth box.

So, the sequence becomes

35, 105, 315, 945,...

Computing the ratios of all the adjacent terms

`(105)/(35)=3,\:\quad (315)/(105)=3,\:\quad (945)/(315)=3`

The ratio of all the adjacent terms is the same and equal to

`r=3`

Thus, the given sequence represents the geometric sequence.

Therefore, we conclude that 35, 105, 315, 945,... is a geometric sequence.