# Write an equation for the nth term of the geometric sequence -2, 10, -50, ...

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embizze | Certified Educator

Write an equation for the nth term of the sequence -2,10,-50,...

First, there are an infinite number of sequences that start with any given finite number of terms. For example, if we had 1,2,4,8,... many people would give the next term as 16 (powers of 2), but the cake number sequence begins 1,2,4,8,15,26; the number of regions cut by n line segments in a circle is 1,2,4,8,16,31, etc...

Assuming that the sequence is formed by multiplying the previous term by -5:

(1) A recursive formula is a(n+1)=-5a(n). (The (n+1)st term is the nth term times -5)

(2) An explicit formula isĀ `a_n=-2(-5)^(n-1)`