Question

Which term of AP, 100, 97, 94, 91,... will be its first -ve term ?

Answer 1

Answer: 35 th term

Solution:

To find the first negative term ,we had to put the formula of nth term with the condition of less than 0

We know that formula is

$T_{n} = a + (n - 1)d \\ \\ a = 100 \\ \\ d = - 3 \\ \\ a + (n - 1)d < 0 \\ \\ 100 + (n - 1)( - 3) < 0 \\ \\ 3(n - 1) >100 \\ \\ n - 1 > \frac{100}{3} \\ \\ n > \frac{100}{3} + 1 \\ \\ n > \frac{103}{3} \\ \\ \bf n >34.3$

as we know that terms can not be fractional,so upto 34 terms all terms are positive

$T_{34} = 100 - 3(34 - 1) \\ \\ T_{34} = 100 - 99 = 1$

So, 35 term is the first negative term of the AP

$\bf T_{35} = - 2$

Hope it helps you.