Question

Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...

Answer 1

Answer: 52

Step-by-step explanation:

To find the 30th number sequence with the given values of: -6,-4,-2,0.

Multiply 30 by 2 because we add 2 to the sequence every time we go up.

30*2 gives us 60, then we subtract however many 2's were in the given sequence.

From -6 to -4 to -2 to 0, we get 8.

60-8 = 52.

Thank you and I hope this helps. Even if my math is wrong somewhere, I got the answer right on my assignment so this is 100% correct.

Answer 2

so hmm -6, -4, -2, 0? what the heck is going on?

well, from -6 to -4, is really a +2 "difference", and from -4 to -2 is the same amount. So to get the next term's value, you simply "add 2", therefore, 2 is the "common difference" in this arithmetic sequence.

let's also notice that -6 is our first fellow.


`\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=2\\ a_1=-6\\ n=13 \end{cases} \\\\\\ a_n=-6+(13-1)2\implies a_(13)=-6+(13-1)2 \\\\\\ a_(13)=-6+(12)2\implies a_(13)=-6+24\implies a_(13)=18`