What is the closed linear form of the sequence 5, 7.5, 10, 12.5, 15,... A) an = 5 + 2.5n B) an = 5 - 2.5n C) an = 2.5 + 2.5n D) an = 2.5 - 2.5n

Answer: Option C)[tex]a_n = 2.5 + 2.5n[/tex]Step-by-step explanation:Note that the sequence increases by a factor of 2.5, that is, each term is the sum of the previous term plus 2.5.[tex]7.5 - 5 = 2.5\\\\10 -7.5 = 2.5\\\\12.5 -10 = 2.5[/tex]therefore this is an arithmetic sequence with an increase factor d = 2.5The linear formula for the sequence [tex]a_n[/tex] is:[tex]a_n = a_1 + d(n-1)[/tex]Where[tex]d = 2.5\\\\a_1 = 5[/tex][tex]a_1[/tex] is the first term of the sequenceSo[tex]a_n = 5 + 2.5(n-1)[/tex][tex]a_n = 2.5 + 2.5n[/tex]The answer is the option C)