Question

Question 17
Which term of the AP 53, 48, 43,…. Is the first negative term?

Answer 1

Given AP is 53, 48, 43, ……
First term (a) = 53 and common difference (d) = 48 – 53 = - 5
Let nth term of the AP be the first negative term.
$i.e.,T_n<0[\because nthtermofanAP,T_n=a+(n-1\left)d\right]$
(a + (n - 1)d) < 0
$\Rightarrow$ 53 + (n - 1)(-5) < 0
$\Rightarrow$ 53 - 5n + 5 < 0
$\Rightarrow$ 58 - 5n < 0 $\Rightarrow$ 5n > 58
$\Rightarrow$ n > 11.6 $\Rightarrow$ n = 12
i.e., ${12}^{th}$ term is the first negative term of the given AP.
$\therefore T_{12}$ = a + (12 - 1)d = 53 + 11 (-5)
= 53 - 55 = -2 < 0