Question

Solve the recurrence relation:

Answer 1

\[ a_{n} = a_{n-1} + n, a_{0} = 1\]

Answer 2

solve what? just plug n =1, 2, 3.... in.

Answer 3

oh, solve for the formula, right? wow... it was 3 years ago when I took this course. hehehe...

Answer 4

yeah

Answer 5

glad you still got it

Answer 6

i know they come out to be 2, 4, 7 but I don't see no pattern there with exponents or anything..... ugh

Answer 7

no your reply!

Answer 8

\[a_1 = a_0+1\\a_2= a_1+2= a_0+1+2=a_0+3\\a_3= a_2+3= a_0+3+3=a_0+6\\.......\\a_n=???\]

Answer 9

All you have to do is interpret the number at the end of each row. You see, at row 2, that is \(a_\color{red}{2}\), then the last number is 3
row 3, \(a_\color{blue}{3}\) then the last number is 6
do some more, you can construct the link between them.
Note: the first term is \(a_0\) always, no need to look at it.

Answer 10

then \(a_{4} = a_{0} + 10 \) and i don't see a link