Question

write a recursive formula for 8,6,4,2,0 then find a14

Answer 1

you're recursion is subtraction by 2.

\[ y_{n+1} = y_n - 2 \]

this then gives you:

\[ y_1 = 8 - 2 = 6 \]
\[ y_2 = 6 - 2 = 4 \]

however you can "solve" this:
\[y_1 = (y_0 - 2)\]
\[y_2 = ((y_0 -2) -2) = y_0 - 4 = y_0 - 2*2\]
\[y_3 = (((y_0 - 2) - 2) - 2) = y_0 -6 = y_0 - 2*3\]

so in general you get:
\[ y(n) = y_0 - 2n\]
so

then at 14 you would get:
\[y(14) = 8 - 2*14 = -20\]