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