Samuel F. answered • 3d

STEM Tutor and PhD Student

Hello Aaron!

If a1 =4, then a2 = 4-3 = 1

a3 = a2 - 3 = 4 - 3 -3 = 4-3*2 = -2

a4 = a3 - 3 = 4 - 3 -3*2 = 4 - 3*3 = 4 - 9 = -5

The formula seem to be: a_{n} = 4 -3*(n-1) . O get a more accurate answer, we need to test of it holds for other values, it will be clear later. Let's consider a_{n+1}.

By the question statement, a_{n+1 }= a_{n} - 3. If our formula is equivalent to this one, the it must be true (because if it's true for a term, it must hold true to the other). By our formula.

a_{n+1} = 4 -3*n

a_{n} = 4 -3*(n-1)

a_{n+1} - a_{n} = -3*n + 3*(n-1) = -3n + 3n -3 = -3

a_{n+1} = a_{n} - 3

Therefore our formula is true.

**a**_{n}** = 4 -3*(n-1) **

Aaron S.

Thank you very much3d