write an explicit definition for the sequence -4,1,6,11...

Question

anonymous · Answer

@mathstudent55

zepdrix · Answer

Hey Belle :)

Hmm this appears to be an arithmetic sequence.
Each term is increasing by the same amount.
How much are we increasing by each time?

anonymous · Answer

5

zepdrix · Answer

Mmm k good.

zepdrix · Answer

If we call the first term $\Large\rm a_1$, then we know that $\Large\rm a_1=-4$.
And then $\Large\rm a_2=-4+5$, yah? :o

anonymous · Answer

yeah because it equals 1 right?

zepdrix · Answer

Mhm :)
To get to further terms in the sequence, we add more 5's.$$\Large\rm a_3=-4+5+5$$$$\Large\rm a_3=-4+5(2)$$

zepdrix · Answer

We would like to write this more `generally` though for our sequence.
We want to know a `formula` for getting the "nTH" term.

anonymous · Answer

So it would be an= -4+5(n) ? the n for what number term it is?

zepdrix · Answer

Notice that for the `third` term, we needed two 5's.
For the `fourth` term, we would add three 5's.
That pattern would repeat.

So for our "nTH" term, we would start with -4 and add (n-1) 5's.

anonymous · Answer

Ooooooh, okay! I got it! Thank you so much!!

zepdrix · Answer

Yay team \c:/