Find an explicit form f(n) for each of the following arithmetic sequences (assume a is some real number and x issome real number).d. a, 2a + 1, 3a + 2, 4a + 3, ...

Answer:The explicit form f(n) is [tex]a_{n} = a +(n-1)(a+1)[/tex]Step-by-step explanation:A sequence is arithmetic if the difference between each consecutive terms is a constant.The explicit formula of an arithmetic sequence is:[tex]a_{n}=a_{1}+(n-1)d[/tex]Where d is the common difference, a1 is the first term of the sequence and an is the nth term.In order to obtain the common difference, you have to subtract two consecutive terms:For the first and second terms:2a+1 - a = a+1For the second and third terms:3a+2 - (2a+1)=Applying the distributive property:3a+2-2a-1= a+1Notice that the difference of any two consecutive terms is the same. Therefore:d=a+1Also, a1=a (The first term)Replacing in the explicit formula:[tex]a_{n} = a +(n-1)(a+1)[/tex]