Question

Which term of the A.P. 105, 101, 97, ........  is the first negative term?

Answer 1

Here a = 105 and d = 101 – 105 = – 4

Let a_n be the first negative term.

`\implies` a_n < 0

`\implies` a + (n – 1)d < 0

`\implies` 105 + (n – 1)(– 4)<0

`\implies` 105 – 4n + 4 <0

`\implies` 109 – 4n < 0

`\implies` 109 < 4n

`\implies` 27.25 < n

The value of n = 28.

Therefore 28^th term is the first negative term of the given A.P.