If the sequence is defined recursively by a₁ = 1 and aₙ = aₙ₋₁ + 2 for n > 1, what is a₄?

To find the value of ( a_4 ) in the given recursive sequence, we start with the initial value and follow the defined recursive relationship.

The sequence is defined as follows:

• The first term ( a_1 = 1 ).

• For any term ( n > 1 ), the term is calculated using the formula ( a_n = a_{n-1} + 2 ).

Now, we can calculate the subsequent terms one by one:

1. For ( n = 2 ):

[

a_2 = a_1 + 2 = 1 + 2 = 3

]

2. For ( n = 3 ):

[

a_3 = a_2 + 2 = 3 + 2 = 5

]

3. Finally, for ( n = 4 ):

[

a_4 = a_3 + 2 = 5 + 2 = 7

]

Thus, the value of ( a_4 ) is 7. This matches the requirement of the recursive relation by consistently adding 2 to the previous term, ensuring the sequence grows in a predictable manner