Question

Which is the first negative term of the arithmetic progression 112, 107,102?

Answer 1

Dear student,

the given AP is 112, 107, 102 ...

First term named as 'a' and common difference as 'd'
here a= 112 and

d= -5(d=a2-a1)

Now we assume that the
the nth term of the given AP be the first negative term
Now look the equation,
Then, an < 0
= a + (n-1) d< 0
= 112 + (n-1) (-5) <0
= 112 - 5n + 5 <0
= 117 - 5n <0
= 117 < 5n
= n< 117 / 5
=n<23.5
= 24 is greater than 23.5 therefore the 24th term is the first negative term

We know that an= a + (n-1) d

Then

a24=a+23×d

By substituting values of a and d

We get a24=-3

Which is the first negative number in this AP

Hope you understood the answer.