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

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

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

Answer»

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