Determine whether each sequence is arithmetric or geometric. Find the next three terms.
1.14, 19, 24, 29,...
geo, 34, 39, 44****
arithmetric, 32,36,41****
arithmetric, 34, 39, 44
The sequence is neither geo nor arith
2.-4,8,-16,32,...
arith, 64, 128, 256****
geo, -64, 128, -256****
geo, -48, 64, -80
The sequence is neither geo nor arith
3.81, 27, 9, 3,...
arith, 0, -3, -6
geo, 0, -3, -6****
geo, 1, 1/3, 1/9****
The sequence is neither geo nor arith
Find the next three terms in the sequence.
4. 3,12,21,30,...
40,50,60
38,46,54****
39,48,57
36,32,39****
5. 30,22,14,6
3,-12,-21****
-1,-8,-15
-1,-2,3
-2,-10,-18****
I PICKED 2 ANSWERS BECAUSE I THOUGHT THEY WERE BOTH RIGHT.
#1 is Arithmetic with d = 5
It is NOT geometric
r = 29/24 = 1.208
r = 19/14 = 1.357
1.208 is NOT 1.357
2.
-4,8,-16,32,...
-4 to + 8 is +12
then it goes DOWN 12
so not arithmetic, different d
now is it geometric?
8/-4 = -2
-16/8 = -2
32/-16 = -2 = r SO GEOMETRIC
next term is
32 * -2 = -64
so the middle one.
I do not understand why you are having trouble with these.
http://www.mathsisfun.com/algebra/sequences-sums-geometric.html
http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html
To determine whether a sequence is arithmetic or geometric, you need to find the common difference or common ratio between consecutive terms.
For the first sequence: 1.14, 19, 24, 29,...
To determine if it's arithmetic, subtract each term from the previous term:
19 - 1.14 = 17.86
24 - 19 = 5
29 - 24 = 5
Since the differences are not constant, it is not an arithmetic sequence.
To determine if it's geometric, divide each term by the previous term:
19 / 1.14 ≈ 16.67
24 / 19 ≈ 1.26
29 / 24 ≈ 1.21
Since the ratios are not constant, it is not a geometric sequence.
Therefore, the first sequence is neither arithmetic nor geometric.
For the second sequence: -4, 8, -16, 32,...
To determine if it's arithmetic, subtract each term from the previous term:
8 - (-4) = 12
-16 - 8 = -24
32 - (-16) = 48
Since the differences are not constant, it is not an arithmetic sequence.
To determine if it's geometric, divide each term by the previous term:
8 / (-4) = -2
-16 / 8 = -2
32 / (-16) = -2
Since the ratios are constant (-2), it is a geometric sequence.
Therefore, the second sequence is geometric.
For the third sequence: 81, 27, 9, 3,...
To determine if it's arithmetic, subtract each term from the previous term:
27 - 81 = -54
9 - 27 = -18
3 - 9 = -6
Since the differences are not constant, it is not an arithmetic sequence.
To determine if it's geometric, divide each term by the previous term:
27 / 81 = 1/3
9 / 27 = 1/3
3 / 9 = 1/3
Since the ratios are constant (1/3), it is a geometric sequence.
Therefore, the third sequence is geometric.
Now, for the next three terms in each sequence:
1. For the first sequence (neither arithmetic nor geometric),
the next three terms could be anything, so there is no unique answer.
2. For the second sequence (geometric),
the common ratio is -2.
So, the next three terms are: -64, 128, -256.
3. For the third sequence (geometric),
the common ratio is 1/3.
So, the next three terms are: 1/9, 1/27, 1/81.
As for the fourth and fifth sequences, please provide the options, and I will explain how to determine the next three terms.