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Case Study – 1
Hari wants to participate in a $200$ m race. He can currently run that distance in $51$ seconds, and with each day of practice, he hopes to take $2$ seconds less than the previous day. He wants to do it in $31$ seconds.
Based on the above information, answer the following questions:
(i) Write the A.P. which represents the above situation.
(ii) Find the minimum number of days he needs to practice to achieve the goal.
(iii) (a) Find the expression for the $n^{th}$ term of the A.P.
OR
(b) If he wants to do it in $21$ seconds, how many minimum days will he take ?
Hari wants to participate in a $200$ m race. He can currently run that distance in $51$ seconds, and with each day of practice, he hopes to take $2$ seconds less than the previous day. He wants to do it in $31$ seconds.
Based on the above information, answer the following questions:
(i) Write the A.P. which represents the above situation.
(ii) Find the minimum number of days he needs to practice to achieve the goal.
(iii) (a) Find the expression for the $n^{th}$ term of the A.P.
OR
(b) If he wants to do it in $21$ seconds, how many minimum days will he take ?
Show SolutionHide Solution↓
Sol. (i) $51, 49, 47, 45, \dots, 31$
(ii) Here $a = 51 \& d = -2$
$31 = 51 + (n - 1) (-2)$
$\Rightarrow n = 11$
So, minimum $11$ days he need to practice to achieve the goal.
(iii) (a) $a_n = 51 + (n - 1) (-2)$
$a_n = 53 - 2n$
OR
(b) $21 = 51 + (n - 1) (-2)$
$n = 16$
So, minimum $16$ days he need to practice to achieve the goal.
(ii) Here $a = 51 \& d = -2$
$31 = 51 + (n - 1) (-2)$
$\Rightarrow n = 11$
So, minimum $11$ days he need to practice to achieve the goal.
(iii) (a) $a_n = 51 + (n - 1) (-2)$
$a_n = 53 - 2n$
OR
(b) $21 = 51 + (n - 1) (-2)$
$n = 16$
So, minimum $16$ days he need to practice to achieve the goal.