Question

Given the sequence: {2, 9, 16, 23, 30…}, a30 = ???

Answer 1

what should i use to solve this

Answer 2

firstly find the recursive formula

Answer 3

let
\(a_0=2\)
\(a_1=9\)
\(a_2=16\)
\(a_3=23\)
....

Answer 4

retriceu can see
\[16=a_2=2*9-2=2a_1-a_0\]\[a_3=2a_2-a_1\]...\[a_n=?\]

Answer 5

7

Answer 6

7 ? what?

Answer 7

a

Answer 8

so a30=212

Answer 9

is it right?

Answer 10

yes it is...

\[a_n=2a_{n-1}-a_{n-2}\]
characterstic equation\[s^2-2s+1=0\] \(s=1\) with multiplicity of 2

so we can write \(a_n=A+Bn\) find A and B u will get A=2 , B=7

\(a_n=2+7n\) so \(a_{30}=2+7*30=212\)