Which one of the following is a geometric sequence?
A. 2, –3, 9⁄2, −18⁄4
B. 0,1,2,3,...
C. 8,4,2,1,1⁄2,1⁄4,... D. –7,10,23,36,..
i think the answer is D
Can please check it ?
Formula for a geometric sequence :
an = a1 * r ^ ( n - 1 )
an is the nth term,
a1 is the first term,
r is the common ratio.
In this case :
a = 8
r = 1 / 2
a1 = 8 * ( 1 / 2 ) ^ ( 1 - 1 )
a1 = 8 * ( 1 / 2 ) ^ 0
a1 = 8 * 1 = 8
a2 = 8 * ( 1 / 2 ) ^ ( 2 - 1 )
a2 = 8 * ( 1 / 2 ) ^ 1
a2 = 8 * 1 / 2 = 4
a3 = 8 * ( 1 / 2 ) ^ ( 3 - 1 )
a3 = 8 * ( 1 / 2 ) ^ 2
a3 = 8 * 1 / 4 = 2
a4 = 8 * ( 1 / 2 ) ^ ( 4 - 1 )
a4 = 8 * ( 1 / 2 ) ^ 3
a4 = 8 * 1 / 8 = 1
a5 = 8 * ( 1 / 2 ) ^ ( 5 - 1 )
a5 = 8 * ( 1 / 2 ) ^ 4
a5 = 8 * 1 / 16 = 1 / 2
a6 = 8 * ( 1 / 2 ) ^ ( 6 - 1 )
a6 = 8 * ( 1 / 2 ) ^ 5
a6 = 8 * 1 / 32 = 1 / 4
An employee makes an hourly rate plus any tips they earn. This tip employee made a total of $400 by working 28 hours last week. If $253 of their total earnings was their tips, what is their hourly rate of pay?
a.
$5.25
b.
$5.61
c.
$8.82
d.
$9.04
Sure! To determine if a sequence is geometric, we need to check if each term can be obtained by multiplying the previous term by a constant factor. Let's check each sequence one by one.
Sequence A: 2, -3, 9/2, -18/4
To determine if this is geometric, let's calculate the ratios between consecutive terms:
-3/2 = -1.5
(9/2)/(-3) = -3/2 = -1.5
(-18/4)/(9/2) = -4
The ratios are not constant, so this sequence is not geometric.
Sequence B: 0, 1, 2, 3, ...
To determine if this is geometric, let's calculate the ratios between consecutive terms:
1/0 = undefined
2/1 = 2
3/2 = 1.5
The ratios are not constant, so this sequence is not geometric.
Sequence C: 8, 4, 2, 1, 1/2, 1/4, ...
To determine if this is geometric, let's calculate the ratios between consecutive terms:
4/8 = 1/2 = 0.5
2/4 = 1/2 = 0.5
1/2 = 0.5
1/4 = 0.25
The ratios are constant (0.5), so this sequence is geometric.
Sequence D: -7, 10, 23, 36, ...
To determine if this is geometric, let's calculate the ratios between consecutive terms:
10/(-7) = -10/7
23/10 = 23/10
36/23 ≈ 1.5652
The ratios are not constant, so this sequence is not geometric.
Hence, you were correct! Sequence C (8, 4, 2, 1, 1/2, 1/4, ...) is the geometric sequence.