Question

Example 4: Sapna's father planted 4 trees in his garden, when he was 22 years old. After that, every year he planted one more tree than the number of trees he planted in the previous year. How many trees will be there in his garden when he will become 40 years old?

Answer 1

Dear student,
Here is the solution of your asked query:
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{be}\mathrm{n}\mathrm{when}\mathrm{he}\mathrm{will}\mathrm{become}40\mathrm{years}\mathrm{old}. \\ \mathrm{Number}\mathrm{of}\mathrm{trees}\mathrm{planted}\mathrm{when}\mathrm{his}\mathrm{age}\mathrm{was}22\mathrm{years}\mathrm{old}=4 \\ \mathrm{Now}\mathrm{according}\mathrm{to}\mathrm{question}\mathrm{we}\mathrm{have}; \\ \mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{planted}\mathrm{at}\mathrm{an}\mathrm{age}\mathrm{of}23=5 \\ \mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{planted}\mathrm{at}\mathrm{an}\mathrm{age}\mathrm{of}24=6 \\ \mathrm{So}\mathrm{here}\mathrm{common}\mathrm{difference}\mathrm{d}=1 \\ \mathrm{first}\mathrm{term},\mathrm{a}=4 \\ \mathrm{number}\mathrm{of}\mathrm{terms},\mathrm{n}=(40-22)+1=19 \\ \mathrm{So}\mathrm{sum}\mathrm{of}\mathrm{n}\mathrm{terms}={\mathrm{S}}_{19}=\frac{19}{2}\left[2\times 4+\left(19-1\right)\times 1\right]=\frac{19}{2}\times 26=247 \\ \mathrm{Therefore}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{at}\mathrm{an}\mathrm{age}\mathrm{of}40\mathrm{years}=247 \end{gathered}$$
Regards