Asked by Lucas
An arithmetic series has first term -50 and common difference 4. How many terms are in the series so that the sum of the series first exceeds 100?
Answers
Answered by
Reiny
Again, use your definition.
you know S(n) = (n/2)(2a + (n-1)d ), so
(n/2)(2a + (n-1)d ) > 100
and you know both a and d
remember that n has to be a whole number, and you will end up with a quadratic inequality.
(n/2)(2a + (n-1)d ) = 100 ,
sub in your values, solve the resulting quadratic for n
<b>round up</b> your n to the next whole number
you know S(n) = (n/2)(2a + (n-1)d ), so
(n/2)(2a + (n-1)d ) > 100
and you know both a and d
remember that n has to be a whole number, and you will end up with a quadratic inequality.
(n/2)(2a + (n-1)d ) = 100 ,
sub in your values, solve the resulting quadratic for n
<b>round up</b> your n to the next whole number
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