Question

Which term of the progression `4, 3 5/7, 3 3/7,` is the first negative term?

Answer 1

Given:

`4, 3 5/7, 3 3/7, ....`

`4 = 28/7, 3 5/7 = 26/7, 3 3/7 = 24/7`

a = `28/7`

= 4

d = `26/7 - 28/7`

= `-2/7`

T_n​ = a + (n − 1)d

`T_n ​= 4 + (n − 1) (-2/7)`

The first negative term occurs when T_n < 0

`4 - 2/7(n -1) < 0`

Multiply both sides by 7:

28 − 2(n − 1) < 0

28 − 2n + 2 < 0

30 − 2n < 0

2n > 30

⇒ n > 15

The smallest integer value of n = 16

The 16th term is the first negative term of the progression.