Question

which term of the ap: 53,48,43........is the first negative term

Answer 1

Hello there~!!

Let the first term be a and the common difference be d.

Hence, a = 53, and d = 48 - 53 = -5

Let the nth term be the first negative term.
Thus,
a + (n-1)d            < 0
=> 53 + (n-1)(-5) < 0
=> 53 - 5n + 5     < 0
=> 58  -  5n         < 0
=> 58                  < 5n
=> 11.6               < n

So, n > 11.6
The nearest whole number greater than 11.6 is 12.

So, 12th term is the first negative term.
Now, what is the negative term?
Let's find out....

..
..
Let it be x

x = a + 11d
=> x = 53 + 11 x (-5)
=> x = 53 - 55
=> x = -2

Hence, the 12th term is the first negative term and the first negative term is -2.


HOPE MY ANSWER IS SATISFACTORY....
THANKS!