Question

anyone wanna help me with this question about arithmetic sequences?

Answer 1

Hey Ellie :)
So to get from the 10th term to the 11th term we add some amount.
\(\Large\rm 32+k\)
to then get from the 11th term to the 12th term, we would add that same amount once again.\[\Large\rm (32+k)+k=106\]

So to get from the 10th to the 12th, we added something twice.

Answer 2

If it's easier this way, maybe you can think of it like slope.
Find the difference in the terms, and divide that by the difference in the term numbers.\[\Large\rm k=\frac{106-32}{12-10}\]

Answer 3

After you have your k value,
You can setup the general form using the information we have:\[\Large\rm a_n=\color{orangered}{a_1}+(n-1)\color{royalblue}{k}\]

Answer 4

thank you!!!!