Question

HELPPP PLSSS Write the equation of the arithmetic sequence defined by a1 = 3 and a4 = 0. (Type your answer in the form an= and please do NOT use spaces.)

Answer 1

`a_n=4-n`

Explanation:

Recall the definition of the general nth term of an arithmetic sequence of common difference "d":

`a_n=a_1+(n-1)\,d`

we can use this formula to find the common difference knowing the first and fourth terms, and then write the general form for the sequence:

`a_n=a_1+(n-1)\,d\\0=3+(4-1)\,d\\0=3+3\,d\\0-3=3\,d\\d=-1`

Then the general form for the nth term of this sequence is:

`a_n=3+(n-1)\,(-1)\\a_n=4-n`