Question

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

Answer 1

Here a = 114, d is common difference 

d = a₃ – a₂ = a₂ – a₁ = –5 

For finding first negative term T_n < 0 

a + (n – 1) d < 0 

114 + (n – 1) (– 5) < 0 

114 – 5n + 5 < 0 

119 – 5n < 0 – 5n < – 119 

5n > 119 

n > 119/5 

n > 23.8 

Therefore first negative term is 24^th term