Write a recursive formula for this sequence:
16, 40, 100, 250.....

Use parenthesis for subscripts. For example, ^an can be written a(n)

Question

Write a recursive formula for this sequence:
16, 40, 100, 250.....

Use parenthesis for subscripts. For example, ^an can be written a(n)

anonymous · Answer

firstly try to find a pattern for $a_0=16$ , $a_1=40$ and $a_2=100$

anonymous · Answer

which states $a_3$ in terms of $a_1$ and $a_0$

anonymous · Answer

for example i see $$100=\frac{40}{2}+5*16$$

anonymous · Answer

ok

anonymous · Answer

how do i find the formula

anonymous · Answer

well as u can see  $$a_2=\frac{a_1}{2}+5a_0$$

anonymous · Answer

sorry forgot to mention some notations
let
$a_0=16$  , $a_1=40$ , $a_2=100$ and $a_3=250$

anonymous · Answer

$$a_2=\frac{a_1}{2}+5a_0$$$$a_3=\frac{a_2}{2}+5a_1$$now u can generalize it

anonymous · Answer

do cross multiply

anonymous · Answer

no just generalize it for $a_n$  in terms of  $a_{n-1}$ and $a_{n-2}$

before that can u tell me what is $a_4$ ?

anonymous · Answer

250

anonymous · Answer

thats $a_3$  
i ask u to find $a_4$

anonymous · Answer

100

anonymous · Answer

but how do i write these in a formula

anonymous · Answer

$$\huge a_n=\frac{a_{n-1}}{2}+5 a_{n-2}$$ for $$\huge n \ge 2$$

anonymous · Answer

is that the formula