Consider the sequence: 3, 8, 13, 18, 23, ...The recursive formula for this sequence is:an = an-1 + 5In a COMPLETE sentence, explain what an and an-1 represent in the formula. Then find a8 . What do you need to know in order to find a8 ?

Answer:see the explanationStep-by-step explanation:we know thatIn an Arithmetic Sequence the difference between one term and the next is a constant called the common differencewe have[tex]3, 8, 13, 18, 23,...[/tex]Let[tex]a_1=3\\a_2=8\\a_3=13\\a_4=18\\a_5=23\\[/tex][tex]a_2-a_1=8-3=5[/tex] ------>[tex]a_2=a_1+5[/tex][tex]a_3-a_2=13-8=5[/tex] ------>[tex]a_3=a_2+5[/tex][tex]a_4-a_3=18-13=5[/tex] ------>[tex]a_4=a_3+5[/tex][tex]a_5-a_4=23-18=5[/tex] ------>[tex]a_5=a_4+5[/tex]sothe common difference between consecutive terms is equal to 5we can rewrite the formula as[tex]a_n=a_(_n_-_1_)+5[/tex] -----> given formula For n > 1wherean is the term that you want to find (position n)a(n-1) is the known term position (n-1)Find a_8For n=8[tex]a_8=a_(_8_-_1_)+5[/tex][tex]a_8=a_7+5[/tex]I need to know a_7or we know thatThe general formula for arithmetic sequence is equal to[tex]a_n=a_1+d(n-1)[/tex] wherean is the term that you want to find (position n)a_1 is the first termd is the common differencen is the number of termswe have[tex]a_1=3[/tex][tex]d=5[/tex]substitute[tex]a_n=3+5(n-1)[/tex] [tex]a_n=3+5n-5[/tex] [tex]a_n=5n-2[/tex] soFor n=8[tex]a_8=5(8)-2[/tex] [tex]a_8=38[/tex]