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# Whats the pattern for 1 -3 9 ? 81 ? -243. ? ?

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Whats the pattern for 1 -3 9 ? 81 ? -243. ? ?

Guest Jan 15, 2015

#3
+18827
+10

Whats the pattern for 1 -3 9 ? 81 ? -243. ? ?

$$\begin{array}{lrcl} n& & & \\ 1& 1 & = & 3^0 \\ 2& -3 &=& (-3)^1 \\ 3& 9 &=& 3^2\\ 4& -27 &=& (-3)^3 \\ 5& 81 &=& 3^4\\ 6&-243 &=& (-3)^5\\ 7&729 &=& 3^6\\ 8&-2187 &=& (-3)^7\\ \dots \end{array} \\ \small{\text{ The formula is: (-3)^{n-1} }}$$

heureka  Jan 15, 2015
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#1
+5

the first item is 1 and the second item is -3 , the difference  between these two numbers are -3/1 =-3

the second item is  3 and the third item is 9, the difference between these two numbers are 9/-3=-3

so the common difference is -3 , the fourth  item should be =3x9=27 and the fifth item 81=-3x-27

so you can find the others by yourself ..........

Guest Jan 15, 2015
#2
+80983
+5

(-1)n+1(3)n-1    ....where n is the nth term.....

CPhill  Jan 15, 2015
#3
+18827
+10
$$\begin{array}{lrcl} n& & & \\ 1& 1 & = & 3^0 \\ 2& -3 &=& (-3)^1 \\ 3& 9 &=& 3^2\\ 4& -27 &=& (-3)^3 \\ 5& 81 &=& 3^4\\ 6&-243 &=& (-3)^5\\ 7&729 &=& 3^6\\ 8&-2187 &=& (-3)^7\\ \dots \end{array} \\ \small{\text{ The formula is: (-3)^{n-1} }}$$