Question 1084171
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In subscript form, the recursive formula would be
*[Tex \LARGE a_{1} = 2]
*[Tex \LARGE a_{n} = -3*\left(a_{n-1}\right)]
Which says "The starting term is *[Tex \Large a_1 = 2]. To get the nth term *[Tex \Large a_n], we need to multiply the previous term *[Tex \Large a_{n-1}] by -3."
In this case, n is some positive whole number (n > 0).


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With function form, we have the same basic format just with different notation
The function form would be
{{{f(1) = 2}}}
{{{f(n) = -3*f(n-1)}}}
where n > 0 is a whole number.


If we plug in n = 2 to get the second term, we get
{{{f(n) = -3*f(n-1)}}}
{{{f(2) = -3*f(2-1)}}} replace every n with 2
{{{f(2) = -3*f(1)}}}
{{{f(2) = -3*(2)}}} Replace f(1) with 2 (since {{{f(1) = 2}}} is defined above)
{{{f(2) = -6}}}
and we get the proper second term, which is -6


If we plug in n = 3 to get the third term, we get
{{{f(n) = -3*f(n-1)}}}
{{{f(3) = -3*f(3-1)}}} replace every n with 3
{{{f(3) = -3*f(2)}}}
{{{f(3) = -3*(-6)}}} Replace f(2) with -6 (since we just found {{{f(2) = -6}}} above)
{{{f(3) = 18}}}
and we get the proper third term, which is 18


The rest of the terms are generated in this recursive fashion.


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