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?

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(52793)   (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 = = 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.

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    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

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Free of charge online textbook in ALGEBRA-II
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Answer by Theo(13342)   (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.

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