Question

In a nursery, 37 plants have been arranged in the first row, 35 in the second, 33 in the third and so on. If there are 5 plants in last row, how many plants are there in the nursery?

Answer 1

The given sequence is: 37, 35, 33 ........., 5

$a=37,d=-2,a_n=5$

$a_n=a+(n-1)d$

$\Rightarrow 5=37+\left(\right(n-1)\times -2$)

$\Rightarrow 5=37+2-2n$

$\Rightarrow 5=39-2n$

$\Rightarrow 2n=34$

$\Rightarrow n=17$

$S_n=\frac{n}{2}(a+a_n)$

$\Rightarrow \frac{17}{2}(37+5)$

$\Rightarrow \frac{17}{2}\times 42$

$=17\times 21$

$=357$