Final answer:
To find a5 for the recursive sequence with a1 = 7 and an = -4an-1 + n, each term up to the fifth must be calculated sequentially. The value of a5 is found to be 1701.
Step-by-step explanation:
The student is asking to find the value of a5 given the recursive sequence where a1 = 7 and an = -4an-1 + n. To find the fifth term, a5, we need to calculate the terms that come before it since it's a recursive sequence.
- a1 is given as 7.
- To find a2, plug n = 2 into the recursion: a2 = -4(7) + 2 = -28 + 2 = -26.
- Next, a3 = -4(-26) + 3 = 104 + 3 = 107.
- Then, a4 = -4(107) + 4 = -428 + 4 = -424.
- Finally, a5 = -4(-424) + 5 = 1696 + 5 = 1701.
Therefore, the value of a5 in the sequence is 1701.