Question

Find common ratio and series sum

Maggie is starting a small farm. In her first year, she harvests 90.000
kilograms of kale. As she gets better at planting, fertilizing and pest control,
each year her harvest increases by 3%. What is her total harvest over the
first 5 years that she owns the farm?
Represent this scenario as a finite geometric series and calculate the
sum.
Enter the total harvest of kale in
kilograms

Answer 1

Her total harvest over the

first 5 years that she owns the farm is 11277 kg

Explanation:

Maggie is starting a small farm. In her first year, she harvests 90.000 kilograms of kale.

As she gets better at planting, fertilizing and pest control,

each year her harvest increases by 3%.

So,

In First year

She owns 90,000 kg

In Second year

She owns 90,000 kg and her harvest is increases by 3%.

i.e.,

90000 × 3 ÷ 100 = 2700

So, The increase in 90,000 kg kale is 2,700

Now,

90,000 + 2,700 = 92,700 kg

In Third year

She owns 92,700 kg and her harvest is increases by 3%.

i.e.,

92700 × 3 ÷ 100 = 2781

So, The increase in 92,700 kg kale is 2781

Now,

92,700 + 2,781 = 95,481 kg

In Fourth year

She owns 95,481 kg and her harvest is increases by 3%.

i.e.,

95481 × 3 ÷ 100 = 2846

So, The increase in 95,481 kg kale is 2846

Now,

95,481 + 2,846 = 98,345 kg

In Fifth year

She owns 98,354 kg and her harvest is increases by 3%.

i.e.,

98354 × 3 ÷ 100 = 2950

So, The increase in 98354 kg kale is 2950

Now,

98354 + 2950 = 101,295 kg

Now,

In First five years She owns

2700 + 2781 + 2846 + 2950 = 11277 kg

Thus, her total harvest over the first 5 years that she owns the farm is 11277 kg

-TheUnknownScientist