Question

Find f(5) for this sequence:

f(1) = 2 and f(2) = 4, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Numerical Answers Expected! help please

Answer 1

@strawberryswing

Answer 2

well.
\(\large\color{black}{ f_3=f_1+f_2+f_{3-1} }\)

\(\large\color{black}{ f_3=2+4+f_{2} }\)

\(\large\color{black}{ f_3=6+4 }\)

\(\large\color{black}{ f_3=10 }\)

Answer 3

then, \(\large\color{black}{ f_4=f_1+f_2+f_{4+1} ~~~\Rightarrow~~f_4=2+4+f_{3} ~~~\Rightarrow~~f_4=6+10=16 }\)

Answer 4

ok thanx

Answer 5

you see the pattern, right. (as the formula says it, but I want to make it visible, just simply)

f(3) = 2+ 4 + 4
f(4) = 2+ 4 + 10
f(5) = 2+ 4 + 16

Answer 6

you can re-write the recursive formula as:
\(\large\color{black}{ f_{n}=6+f_{n-1} }\)

Answer 7

in other words, \(\large\color{black}{ d=6 }\)

Answer 8

ok thank u

Answer 9

yw

Answer 10

btw, do you need a latex for sigma notation in text?

Answer 11

`\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ \infty } ~ f(n)}\)`

\(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ \infty } ~ f(n)}\)