# What is the first positive term of -118-111-104-...?

`-118,-111,-107,.....`

`T_1 = -118`

`T_2 = -111`

`T_3 = -107`

` T_2-T_1 = -111-(-118) = 7`

`T_3-T_2 = -107-(-111) = 7`

So the sequence is a arithmetic series with initial term -118 and common difference 7.

`a = -118`

`d = 7`

In a arithmetic series...

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`-118,-111,-107,.....`

`T_1 = -118`

`T_2 = -111`

`T_3 = -107`

` T_2-T_1 = -111-(-118) = 7`

`T_3-T_2 = -107-(-111) = 7`

So the sequence is a arithmetic series with initial term -118 and common difference 7.

`a = -118`

`d = 7`

In a arithmetic series with initial term 'a' and common difference 'd' the nth term `T_n` is given by;

`T_n = a+(n-1)d`

When it comes to the first positive term;

`T_n > 0`

`a+(n-1)d > 0`

`-118+(n-1)*7 > 0`

`7(n-1) > 118`

`7n > 125`

` n > 125/7`

` n > 17.85`

n is always a positive integer. Therefore n = 18

So the first positive term of the arithmetic series is in the 18th term.

Approved by eNotes Editorial Team