Given arithmetic progresion $20,17,14,\ldots$
Find smallest value of $n$ so $y_n<0$.
I can find value of $n$ by mind , but do not know how to write the solution.
Answer
Assuming $y_0=20$, your arithmetic progression has closed form
$$y_n=20-3n$$
Now let us solve the following inequality.
$$0>20-3n$$
$$3n>20$$
$$n>\frac{20}{3}=7-\frac{1}{3}$$
The minimum integer value of $n$ that satisfies the condition is
$n=7$.
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