HOW TO CHECK IF THE GIVEN SEQUENCE IS GEOMETRIC OR NOT
How to check if the given sequence is geometric or not ?
- If the common ratios of the given sequence are equal, then we can decide that the given sequence is a geometric progression.
- If the common ratios are not equal, then the given sequence is not a geometric progression.
To find the common ratio, we use the formula
r = a2/a1 (or) r = a3/a2
What is geometric progression ?
A Geometric Progression is a sequence in which each term is obtained by multiplying a fixed non-zero number to the preceding term except the first term.
The fixed number is called common ratio. The common ratio is usually denoted by r.
Example 1 :
Find out which of the following sequences are geometric sequences . For those geometric sequences, find the common ratio.
1/2, 1/3, 2/9, 4/47,...........
Solution :
|
r = t2/t1 r = (1/3) / (1/2) r = 2/3 ----(1) |
r = t3/t2 r = (2/9) / (1/3) r = 2/3 ----(2) |
Since the common ratios are same, the given sequence is a geometric sequence. The required common ratio is 2/3.
(ii) 12, 1, 1/12, ............
Solution :
|
r = t2/t1 r = 1/12 ----(1) |
r = t3/t2 r = (1/12) / 1 r = 1/12 ----(2) |
Since the common ratios are same, the given sequence is a geometric sequence. The required common ratio is 1/12.
(iii) √2, 1/√2, 1/2√2,...........
Solution :
|
r = t2/t1 r = (1/√2)/√2 r = 1/2 ----(1) |
r = t3/t2 r = (1/2√2) / (1/√2) r = 1/2 ----(2) |
Since the common ratios are same, the given sequence is geometric progression.
The required common ratio is 1/2.
(iv) 0.004, 0.02, 1, ..........
Solution :
t1 = 0.004, t2 = 0.02 and t3 = 1
|
r = t2/t1 r = 0.02 / 0.004 r = 20 / 4 r = 5 ----(1) |
r = t3/t2 r = 1 / 0.02 r = 100/2 r = 50 ----(2) |
Since the common ratios are not same, the given sequence is not geometric progression.
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