1. ## recurrence formula

Find the explicit formula for the recursive sequence using backtracking
d1 = 3
dn= -2dn-1

I’m thinking I will have (-6, 12, -24, 48,…..)
dn = -2dn-1
= -2dn-1 + 1
= -2 (-2dn-1 +1) +1

but I do not know what else to do to end with a formula. Please show me what my formula will be

* all the (n-1) should be subscripts, do know how to get it to subscript here in this window

2. Hello, CPR!

Find the explicit formula for the recursive sequence using backtracking:
. . $\displaystyle d_1 \:=\:3,\;\;\;d_n\:=\:\text{-}2\!\cdot\!d_{n-1}$

I’m thinking I will have: .$\displaystyle 3,\:\text{-}6,\:12,\:\text{-}24,\:48,\:\hdots\qquad{\color{blue}\text{Right!}}$
I'm not familiar with "backtracking".

This is a geometric sequence with first term $\displaystyle a= 3$, common ratio $\displaystyle r = \text{-}2$

The general term is: . $\displaystyle d_n\;=\;3\cdot(\text{-}2)^{n-1}$

3. Thanks.
but explain to me why the subscript n-1 is now the superscript in the general term formula.