.
This sequence is the geometric progression with the first term 2187 = and the common ratio of .
To find the number of the term in this progression, write an equation for the general term of a GP
= .
In your case this formula takes the form
= , or
= .
From this equation
-2 = 7 - (n-1)
-2 = 7 - n + 1
-2 = 8 - n
n = 8 + 2 = 10.
ANSWER. is the 10-th term in this geometric progression.
To check my answer, you may write this sequence of indexes from 7 to -2 inclusive
7, 6, 5, 4, 3, 2, 1, 0, -1, -2
and count that the index (-2) is the 10-th member in this sequence.
Solved.
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On geometric progressions, see introductory lessons
- Geometric progressions
- The proofs of the formulas for geometric progressions
- Problems on geometric progressions
- Word problems on geometric progressions
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Geometric progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.