The Government of India is planning to plant 6000 trees in various parts of cities within a span of 10 years. They planted 500 in the first year and increased by 20 every year. After 10 years, how much more trees they will have to plant in order to reach the required target?

To find out how many more trees the Government of India needs to plant after 10 years to reach their target of 6000 trees, we first need to calculate the number of trees planted each year.

In the first year, they planted 500 trees. From the second year onwards, the number of trees planted increased by 20 each year.

To calculate the number of trees planted in the second year, we add 20 to the number planted in the first year:
500 + 20 = 520

To calculate the number of trees planted in the third year, we add 20 to the number planted in the second year:
520 + 20 = 540

We can continue this pattern to calculate the number of trees planted for each year until the 10th year:

Year 2: 520
Year 3: 540
Year 4: 560
Year 5: 580
Year 6: 600
Year 7: 620
Year 8: 640
Year 9: 660
Year 10: 680

Now, let's calculate the total number of trees planted after 10 years:
500 + 520 + 540 + 560 + 580 + 600 + 620 + 640 + 660 + 680 = 6000

We can see that after 10 years, the Government of India has already planted the required target of 6000 trees. Therefore, they do not need to plant any more trees to reach their goal.

To calculate how much more trees the government will have to plant in order to reach the required target, we need to find the total number of trees planted within 10 years and then subtract it from the target.

In the first year, the government planted 500 trees. Each subsequent year, they increased the number of trees planted by 20. So, in the second year, 500 + 20 = 520 trees were planted. In the third year, 520 + 20 = 540 trees were planted. This pattern continues until the 10th year.

To find the total number of trees planted in 10 years, we can use the arithmetic series formula:

\(S_n = \frac{n}{2} \left(2a + (n-1)d \right)\)

Where:
\(S_n\) is the sum of the series (total number of trees planted in 10 years)
\(n\) is the number of terms (in this case, 10)
\(a\) is the first term (500)
\(d\) is the common difference (20)

\(S_{10} = \frac{10}{2} \left(2 \times 500 + (10-1) \times 20 \right)\)

\(S_{10} = 5 \left(1000 + 9 \times 20 \right)\)

\(S_{10} = 5 \left(1000 + 180 \right)\)

\(S_{10} = 5 \times 1180\)

\(S_{10} = 5900\)

So, the government will have planted a total of 5900 trees in 10 years.

To find out how much more trees they will have to plant to reach the required target of 6000 trees, we subtract the total number of trees planted from the target:

\(6000 - 5900 = 100\)

Therefore, the government will have to plant 100 more trees to reach their target of 6000 trees.

a = 500

d = 20
S10 = 10/2 (2a+9d)
subtract S10 from 6000