A sequence is defined recursively by \( f(1) = 16 \) and \( f(n) = f(n-1) + 2n \). Find \( f(4) \).

1) 32
2) 30
3) 28
4) 34

f ( 1 ) = 16 an d f ( n ) = f ( n − 1 ) + 2 n f ( 2 ) = f ( 1 ) + 2 ⋅ 2 = 16 + 4 = 20 f ( 3 ) = f ( 2 ) + 2 ⋅ 3 = 20 + 6 = 26 f ( 4 ) = f ( 3 ) + 2 ⋅ 4 = 26 + 8 = 34
A n s . 4 )

Answered by kate200468 | 2024-06-10

The value of the recursively defined sequence at the fourth term, f(4), is calculated using the given relation to be 34. Option 4) is the correct answer.
The student is asking to find the value of a recursively defined sequence at the fourth term (f(4)). The sequence is defined as f(1)=16 and for n > 1, f(n)=f(n-1)+2n. We find the successive terms up to f(4) using the given recurrence relation:
f(1) = 16 (given)
f(2) = f(1) + 2*2 = 16 + 4 = 20
f(3) = f(2) + 2*3 = 20 + 6 = 26
f(4) = f(3) + 2*4 = 26 + 8 = 34
Therefore, f(4) is 34, which corresponds to option 4 in the question. This is the final answer to the student's question.

Answered by Burger1123 | 2024-06-24

The value of the function f ( 4 ) is calculated as 34, making the correct answer option 4. This is derived from the recursive sequence formula given in the problem. We worked through the recursive definitions step-by-step to arrive at this final answer.
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Answered by kate200468 | 2024-11-01