Solve It...7

Computer Science Level 1

f(3) = 25

f(4) = 41

f(5) = 61

f(6) = 85

f(7) = 113

Find the value of f(9)?

155 193 194 165 181 655

1 solution

Caleb Townsend
Mar 5, 2015

These are the centered square numbers, $2n(n+1) + 1$ $2\times 9\times 10 + 1 = \boxed{181}$ If you are unfamiliar with the sequence, each term is the sum of two consecutive squares. Another formula for $f(n)$ is $n^2 + (n+1)^2$

How do you get all of them???

tanveen dhingra - 6 years, 3 months ago

Do you mean how does the formula work for all of the other numbers in the problem?
$f(3) = 2\times3\times4+1 = 25$
$f(4) = 2\times4\times5+1 = 41$
$f(5) = 2\times5\times6+1 = 61$

Caleb Townsend - 6 years, 3 months ago

No....I mean that how do you know the solutions of all my analogy problems??

tanveen dhingra - 6 years, 3 months ago

@Tanveen Dhingra – Well with this one, I was familiar with the numbers beforehand. My algebra teacher showed them to me as an easy proof assignment when I was in high school.

But for the others, it is a matter of spending a couple minutes to find the pattern that always works! As a kid, I got interested in math because I found patterns to logically explain operations like multiplication and exponentiation. I suppose I have always been interested in patterns.

Caleb Townsend - 6 years, 3 months ago

@Caleb Townsend – Ohh...that's great!!

tanveen dhingra - 6 years, 3 months ago

Solve It...7

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