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vredina [299]
3 years ago
6

Find the number of terms in the geometric progression 7,21,63,..., 45927.

Mathematics
2 answers:
Doss [256]3 years ago
6 0
The rule is times 3

7 x 3 = 21
21 x 3 = 63

and so on until 45927
Degger [83]3 years ago
4 0
What lists are the easiest to count? If you were given a list like 1, 2, 3, 4, ... , 20, it would be pretty easy to determine that there were 20 terms in the sequence. We can transform most sequences to that form to make our job of counting terms a lot easier.

First, we notice that the terms all seem to be multiples of 7. We can start to simplify our list by <em>dividing</em> each term by 7:

7,21,63,\dots,45927\rightarrow1,3,9,\dots,6561

Looking at our new list, you might notice that our numbers all seem to be <em>powers of 3</em>. 1=3^0,3=3^1,9=3^2, and you can verify that 6561=3^8

We can now transform our list again, replacing each term with its corresponding power:

1,3,9,\dots,6561\rightarrow0,1,2,\dots,8

Now, we simply add 1 to each term and:

0,1,2,\dots,8\rightarrow1,2,3,\dots,9

Voila! There are 9 terms in the sequence.
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