Given the Recursive Formula: a1 = 5 a4 = an-1 + 2 a) What term is this formula solving for? b) What should be in place of the n-1? The choices are 3 and 4

Answer 1

a) The recursive formula you've provided is solving for the term \( a_n \), where \( n \) is the position of the term in the sequence.

b) To determine what should be in place of \( n-1 \) in the term \( a_{n-1} \), we have to consider the recursive relationship given:

• The formula specifies that \( a_4 = a_{n-1} + 2 \).

For this relation to hold true, \( n \) must equal 4 since \( a_4 \) is being defined in terms of the previous term in the sequence. Therefore, \( n - 1 = 4 - 1 = 3 \).

So, the answer to (b) is 3.

Thus:

• a) The formula is solving for \( a_n \).
• b) The correct value to replace \( n-1 \) is 3 (making it \( a_3 \)).