Question

Which term of the sequence 114, 109, 104, ... is the first negative term?

 

Answer 1

Here, A.P is 114, 109, 104, ..

So, first term, a = 114 

Now,

Common difference (d) =  a₁ - a

= 109 - 114 

= -5

Now, we need to find the first negative term,

 a_n < 0

114 + (n-1) (-5) < 0

     114 - 5n + 5 < 0

          119 - 5n < 0

                 5n > 119 

Further simplifying, we get,

n > `119/5`

n > 23 `4/5`

n ≥ 24                                  (as n is a natural m=number) 

Thus, n = 24 

Therefore, the first negative term is the  24^th term of the given A.P.