Question

A sequence starts at 400 and 70 is subtracted each time.
400, 330, 260,
What are the first two numbers in the sequence that are less than zero?​

Answer 1

Given : A sequence starts at 400 and 70 is subtracted each time.

400, 330, 260,

To Find : What are the first two numbers in the sequence that are less than zero

Solution:

A sequence starts at 400

First term a = 400

d = common difference  =  - 70

aₙ  = a + (n-1)d

=> aₙ = 400 + (n - 1)(-70)

=>aₙ = 400 - 70n  + 70

=> aₙ = 470 - 70n

470 - 70n  < 0

=> 70n > 470

=> n > 470 /70

=> n > 47/7

=>  n = 7

7th term =  400  + 6(-70)  =  - 20

8th Term = -20 - 70 = -90

first two numbers in the sequence that are less than zero  

are - 20  & - 90

7th & 8th terms

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