Question

write a formula for the apparent nth term of the sequence -1, 2, 7, 14, 23

Answer 1

bet it is a square of some kind
there is a snap way to do it but i forget so we can grind it out

Answer 2

@Callisto do you recall how to do this an easy way?

Answer 3

\[ \large 2=-1+3 \]
\[ \large 7=2+5 \]
\[ \large 14=7+7 \]
\[ \large 23=14+9 \]

Answer 4

I think I haven't learnt the way you mentioned, but I'm thinking if this works
-1 , 2 , 7, 14, 23
+ 3 , +5 , +7 ,+9

Answer 5

try add one, square, subtract 2

Answer 6

well actually i started at 0

Answer 7

\[ \large a_1=-1 \]
\[ \large a_2=-1+3=-1+(2\cdot2-1)=2 \]
\[ \large a_3=2+5=2+(2\cdot3-1)=7 \]
\[ \large a_4=7+7=2+(2\cdot4-1)=14 \]

Answer 8

yes the pattern is clear, and it gives you a square because the differences are linear, like saying the derivative of a quadratic is a line

Answer 9

Wow!
-1 = 1^2 -2
2 = 2^2 - 2
7 = 3^2 - 2
14 = 4^2 - 2
23 = 5^2 -2
><!!!

Answer 10

terms are \(a_1=-1, a_2=2, a_3=7, a_4=14, a_5=23\) like saying \(f(1)=-1, f(2)=2, f(3)=7, f(4=14,f(5)=23\) and so
\(f(x)=x^2-2\)

Answer 11

there is a snappy way to do this without guessing but i forget
in any case it is \(a_n=n^2-2\)

Answer 12

thanks

Answer 13

^^ Don't give answer :P