Let an be the sum of the first n positive odd integers.(a) List out at least the first 4 terms of the sequences. Be sure to use proper notation.(b) Give the closed/explicit formula for this sequence. Be sure to use proper notation.(c) Give the recursive formula for this sequence. Be sure to use proper notation.

Answer: A) The first 4 terms of the sequences are: [tex]a_{1} =16[/tex], [tex]a_{2} =24[/tex], [tex]a_{3} =32[/tex] and [tex]a_{4} =40[/tex].B) An explicit formula for this sequence can be written as: [tex]a_{n} =8*(n+1)[/tex]C) A recursive formula for this sequence can be written as:[tex]\left \{ {{a_{1} =16} \atop {a_{n} =a_{n-1}+8}} \right.[/tex]Step-by-step explanation:A) You can find the firs terms of this sequence simply selecting an odd integer and summing the consecutive 3 ones:[tex]a_{n} = Odd_{n}+Odd_{n+1}+Odd_{n+2}+Odd_{n+3}[/tex] (a.1)[tex]a_{1}=1+3+5+7=16[/tex][tex]a_{2}=3+5+7+9=24[/tex][tex]a_{3}=5+7+9+11=32[/tex][tex]a_{4}=7+9+11+13=40[/tex]B) Observe the sequence of odd numbers 1, 3, 5, 7, 9, 11, 13(...). You can express this sequence as:[tex]Odd_{n}=(2*n-1)[/tex] (b.1)If you merge the expression b.1 in a.1, you obtain the explicit formula of the sequence:[tex]a_{n} = Odd_{n}+Odd_{n+1}+Odd_{n+2}+Odd_{n+3}[/tex] (a.1)[tex]a_{n} = (2*n-1)+((2*(n+1)-1))+((2*(n+2)-1))+((2*(n+3)-1))[/tex] (b.2)[tex]a_{n} = 8*n+8[/tex] (b.3)[tex]a_{n} =8*(n+1)[/tex] (b.s)C) The recursive formula has to be written considering an initial term and an N term linked with the previous term. You can see an addition of 8 between a term and the next one. So you can express each term as an addition of 8 with the previous one. Therefore, if the first term is 16:[tex]\left \{ {{a_{1} =16} \atop {a_{n} =a_{n-1}+8}} \right.[/tex] (c.s)