Question

How do I find the terms?

Answer 1

A(n+1) = A(n)+4 <--- is a way to say, to get the next term, ADD 4 to the current one, whist A(1) = -2, is a way to say, the first term is -2.


`\bf n^(th)\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=4\\ a_1=-2\end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=-2+(2-1)4\\ 3&a_3=-2+(3-1)4\\ 4&a_4=-2+(4-1)4\\ 5&a_5=-2+(5-1)4 \end{array}`

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A(n)= 1/4 * A(n) is just a way of saying, you get the next term by multiplying the current one by 1/4, and A(1) = 8, simply means the first term's value is 8.


`\bf n^(th)\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^(n-1)\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=(1)/(4)\\ a_1=8 \end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=8\left( (1)/(4) \right)^(2-1)\\\\ 3&a_3=8\left( (1)/(4) \right)^(3-1)\\\\ 4&a_4=8\left( (1)/(4) \right)^(4-1)\\\\ 5&a_5=8\left( (1)/(4) \right)^(5-1)\\ \end{array}`