SOLUTION: A plant grows 1.67 cm in its first week. Each week it grows by 2% more than it did the week before. By how much does it grow in twenty weeks, including the first week?

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Question 1163016: A plant grows 1.67 cm in its first week. Each week it grows by 2% more
than it did the week before. By how much does it grow in twenty weeks,
including the first week?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is the sum of the first 20 terms of the geometric progression

with the first term of 1.67 cm and the common ratio of 1.02



    Sum = 1.67%2A%28%281.02%5E20-1%29%2F%281.02-1%29%29 = 40.58 cm.      ANSWER

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

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Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this looks like a geometric progression.
it grows by 1.67 the first week.
it grows by 1.67 * 1.02 the second week.
this continues until the 20th week.
this sound like the sum of a geometric progression.
the formula for that is Sn = A1 * (1 - r^n) / (1 - r)
A1 = 1.67
r = 1.02
n = 20
S20 = 1.67 * (1 - 1.02^20) / (1 - 1.02) = 1.67 * -.485947396 / -.02 = 40.57660756.
to see the progression week by week, view the following.


you can see that the growth in the first week was 1.67 centimeters fpr a total of 1.67 centimeters; the growth in the second week was 1.7034 centimeters for a total of 3.3734 centimeters; the growth in the third week was 1.737468 centimeters for a total of 5.110868 centimeters; etc.....

after the first week, each week's growth was 2% higher than the growth in the week before.
1.67 * 1.02 = 1.7034; 1.7034 * 1.02 = 1.737468; etc.....

your solution is a total growth of 40.57660756 centimeters in 20 weeks.