Which sequences are geometric? Select three options.
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ...
Answers
Answer:
Answer:
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
8, 0.8, 0.08, 0.008, ...
Explanation:
A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio.
now check all the sequence one by one.
For sequence –2.7, –9, –30, –100, .
For sequence –2.7, –9, –30, –100, ...
r =
=
=
We see that, all the ratios are same.
So this is geometric sequence.
For sequence –1, 2.5, –6.25, 15.625, ...
r =
This is also geometric sequence.
For sequence 9.1, 9.2, 9.3, 9.4, ...
In this sequence, common ratio is not same.
So, it is not a geometric sequence.
For sequence 8, 0.8, 0.08, 0.008, ...
Common ratio is same so, it is geometric sequence.
For sequence 4, –4, –12, –20
Common ratio is not same. So, it is not geometric sequence .
Step-by-step explanation:
Given : sequences
To Find : geometric sequences
Solution:
Geometric sequence
A sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.
a , ar , ar² , ... , arⁿ⁻¹
The nth term of a geometric sequence with the first term a and the common ratio r is given by: aₙ = arⁿ⁻¹
Sum is given by Sₙ = a(rⁿ - 1)/(r - 1)
Sum of infinite series is given by a/(1 - r) where -1 < r < 1
Geometric Series
The sum of the terms of a geometric sequence is called a geometric series.
Checking for ratio between consecutive terms
–2.7, –9, –30, –100, ...
-9/(-2.7) = 10/3
-30/(-9) = 10/3
-100/(-30) = 10/3
common ratio = 10/3
Hence Geometric Sequence
–1, 2.5, –6.25, 15.625, ...
2.5/(-1) = -6,25/(2.5) = 15.625/(-6.25) = - 2.5
common ratio = -2.5
=> Geometric Sequence
9.1, 9.2, 9.3, 9.4, ...
no common ratio ( but common difference 0.1 hence in AP)
8, 0.8, 0.08, 0.008, ...
0.8/8 = 0.08/0.8 = 0.008/0.08 = 0.1
Hence common Ratio
so Geometric Sequence
4, –4, –12, –20, ...
-4/4 = - 1
-12/(-4) = 3
No common ratio
So Geometric sequence are
–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
8, 0.8, 0.08, 0.008, ...
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