A(n) = -5 + 6(n - 1)a(n)=−5+6(n−1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, min
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We know that is a parabola, concave up, with vertex in the origin
So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.
Here's the examples:
- The horizontal line
intercepts the parabola twice: the system
is solved by
- The horizontal line
intercepts the parabola only once: the system is
which yields
which is a repeated solution
- The horizontal line
intercepts the parabola only once: the system is
which yields
which is impossible, because a squared number can't be negative.