Question

Arithmetic Progression....
what is the smallest number of terms which must be taken for their sum to be negative ?

Answer 1

the question seems to be missing some information.
e.g. if the arithmetic progression started as -10, -5, 0 ...
then you only need one term for the sum to be negative

Answer 2

the formula for the sum of an AP is given as:\[S_n=\frac{n}{2}(2a_1+(n-1)d))\]so, for the sum to be negative, you need the following condition:\[\frac{n}{2}(2a_1+(n-1)d))\lt0\]

Answer 3

and this depends on \(n\), \(a_1\) and \(d\)

Answer 4

what is the smallest number of terms which must be taken for their sum to be negative ?
calculate the sum exactly .

Answer 5

@asnaseer

Answer 6

I have outlined above my understanding of the problem. Do you agree with my conclusions?