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A sequence has a term 0 of 125 and was decreasing by 6%. What is the explicit equation for this sequence?
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As described, this sequence is a geometric progression with the starting term = 125 and
the starting index "0" (zero). The common ratio of the progression is r = 1-0.06 = 0.94.
Had it have a starting index 1, an explicit formula would be
= .
But since our starting index is 0 (shifted one unit to the left), an explicit formula for the n-th term
of our sequence takes the form
= . ANSWER
CHECK. To check, calculate several starting terms using the formula and then compare the results
with the description
= ; = ; = .
It is consisted with the wording description.
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.