Find the 30th term in the sequence: 18,15,12

Mathematics

2 answers:

r-ruslan [8.4K]3 years ago

8 0

Since it is going down a constant rate (-3) keep subtracting 3 until you get to the 30th term.

jolli1 [7]3 years ago

8 0

Hmmm 18, 15, 12? what's going on? wait a second, 15 is 18-3, and 12 is 15 -3, so... to get the next number is really just subtracting 3 from the current one, meaning, is an arithmetic sequence, the first term's value is 18, and the common difference is -3.

now, what is the 30th term anyway?

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=18\\
d=-3\\
n=30
\end{cases}
\\\\\\
a_n=18+(30-1)(-3)\implies a_{30}=18+(30-1)(-3)
\\\\\\
a_{30}=18-87\implies \boxed{a_{30}=-69}$

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