AQR sequence RV_U4

Front

Define a recursive formula.

Back

A recursive formula defines each term of a sequence using the preceding term(s). It requires knowledge of previous terms to compute the next term.

Front

What is an explicit formula?

Back

An explicit formula allows the computation of any term in a sequence directly without needing to know the previous terms.

Front

Find the first five terms of the sequence defined by the recursive formula: a_n+1 = a_n + 5, where a₁ = 1.

Back

1, 6, 11, 16, 21

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.

Front

Write the recursive formula for the sequence: 3, 6, 9, 12, ...

Back

a_n+1 = a_n + 3

Front

Find the first four terms of the sequence defined by: a_n+1 = a_n * 2, where a₁ = 1.

Back

1, 2, 4, 8

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be expressed as: a_n = a₁ + (n-1)d, where d is the common difference.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be expressed as: a_n = a₁ * r^(n-1), where r is the common ratio.

Front

Find the first five terms of the sequence defined by: a_n+1 = a_n + 4, where a₁ = -3.

Back

-3, 1, 5, 9, 13

Front

What is a common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term of a geometric sequence is multiplied to obtain the next term.