I am learning Mathematics from Khan Academy. I see this explicit formula in arithmetic sequence:
f(n) = 3 - 4(n-1)
I have to find which term in the sequence = -65
I found it out by crude methods of calculating f(10), f(20) etc, it is 18th term. My question is why I can't solve it by using this method.
f(n) = -65, Therefore, -65 = 3 - 4(n -1)
Why it does not work this way ?
Of course you can do it that way.
$$-65= 3-4(n-1)$$
$$-65-3=-4(n-1)$$
$$68 = 4(n-1)$$
Solving for $n$ would give us $n=18$.
Solving is a better way than enumeration or binary search.