Sequence of Arithmetic

Question

Tell whether the sequence is arithmetic.

Tell the common difference.

If the sequence is arithmetic, write a function rule to represent it.

3,7,11,15,...

Answer 1

Since each new term is exactly four more than its predecessor, this is an arithmetic sequence; a₁ = 3, d=4.

THEREFORE a(n) = a(1) + 4(n-1) where is a SUBSCRIPT, n being any POSITIVE INTEGER. This is a recursive rule for a discrete function (not a continuous function of a real variable).