Answer:
[tex]a_{13}=2(13)+13=39[/tex]
39 is the 13th term
Step-by-step explanation:
Okay so essentially the [tex]a_n[/tex] is just a substitute for x.
See how in the equation they put n into the x spot:
[tex]y=mx+b\\a_n=mn+b\\a_n=2n+13[/tex]
They changed the variable names:
[tex]y=a_n\\m=2\\n=x\\b=13[/tex]
Now we know what the n actually means, plus when they ask about the terms youre trying to find it's based off of that n:
When they say, 13 term, they mean [tex]a_{13}[/tex] which would be the 13th answer in the series. So the first term would be based off of [tex]a_1[/tex]
[tex]a_1=2(1)+13\\a_1=15[/tex]
So whatever number is in the n position by a is what you'll be plugging into the x spot.
[tex]y=mx+b\\a_n=2n+13\\a_1=2(1)+13=15\\a_2=2(2)+13=17\\a_3=2(3)+13=19\\a_4=2(4)+13=21\\a_5=2(5) +13=23\\a_6=2(6)+13=25\\a_7=2(7)+13=27\\a_8=2(8) +13=29\\a_9=2(9)+13=31\\a_{10}=2(10)+13=33\\a_{11}=2(11)+13=35\\a_{12}=2(12)+13=37\\a_{13}=2(13)+13=39[/tex]
These are all the answers leading up to the 13th term they asked for, and you can continue thus same equation with whatever number you can put into the n space.
