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A school has decided to plant some endangered trees on $51^{st}$ World Environment Day in the nearest park. They have decided to plant those trees in few concentric circular rows such that each succeeding row has $20$ more trees than the previous one. The first circular row has $50$ trees.
Based on the above given information, answer the following questions :
(i) How many trees will be planted in the $10^{th}$ row?
(ii) How many more trees will be planted in the $8^{th}$ row than in the $5^{th}$ row?
(iii) (a) If $3200$ trees are to be planted in the park, then how many rows are required ?
OR
(b) If $3200$ trees are to be planted in the park, then how many trees are still left to be planted after the $11^{th}$ row?
Based on the above given information, answer the following questions :
(i) How many trees will be planted in the $10^{th}$ row?
(ii) How many more trees will be planted in the $8^{th}$ row than in the $5^{th}$ row?
(iii) (a) If $3200$ trees are to be planted in the park, then how many rows are required ?
OR
(b) If $3200$ trees are to be planted in the park, then how many trees are still left to be planted after the $11^{th}$ row?
Show SolutionHide Solution↓
Here $a = 50$ and $d = 20$
(i) Number of trees planted in $10^{th}$ row $= a_{10} = 50 + 9 \times 20 = 230$
(ii) $a_8 - a_5 = 3 \times 20 = 60$
(iii) (a) Let $S_n = 3200$
$\Rightarrow \frac{n}{2}[2 \times 50 + (n-1) \times 20] = 3200$
$\Rightarrow n^2 + 4n - 320 = 0$
$\Rightarrow (n + 20)(n - 16) = 0$
$n \neq -20$
$\therefore n = 16$
Hence, required number of rows are $16$
OR
(iii) (b) Required number of trees $= S_n - S_{11}$
$= 3200 - \frac{11}{2}[2 \times 50 + 10 \times 20]$
$= 3200 - 1550$
$= 1650$
Hence, number of trees left are $1650$
(i) Number of trees planted in $10^{th}$ row $= a_{10} = 50 + 9 \times 20 = 230$
(ii) $a_8 - a_5 = 3 \times 20 = 60$
(iii) (a) Let $S_n = 3200$
$\Rightarrow \frac{n}{2}[2 \times 50 + (n-1) \times 20] = 3200$
$\Rightarrow n^2 + 4n - 320 = 0$
$\Rightarrow (n + 20)(n - 16) = 0$
$n \neq -20$
$\therefore n = 16$
Hence, required number of rows are $16$
OR
(iii) (b) Required number of trees $= S_n - S_{11}$
$= 3200 - \frac{11}{2}[2 \times 50 + 10 \times 20]$
$= 3200 - 1550$
$= 1650$
Hence, number of trees left are $1650$