arithmetic sequence (Algebra 1, Khan Academy)

Question

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 ?

I think it's better if you do it that way, finding n is alway better than just brute forcing it. — The Integrator, Mar 28 '18 at 06:46

score 0 · Accepted Answer · answered Mar 28 '18 at 06:38

0

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.

answered Mar 28 '18 at 06:38

Siong Thye Goh

1 Answers1