ID: 340

Provide a formula for computing the nth term in the given sequence 5, 14, 23, 32, 41, ...

Aligned LLM's Response:

The given sequence is the F ib on acci sequence , in which each term is the sum of the two preceding terms . The n th term in the F ib on acci sequence can be computed using the formula : \n \n F ( n ) = ( phi ^ n - (- phi )^ (- n )) / sq rt ( 5 ) \n \n where ph i is the golden ratio , approximately equal to 1 . 6 1 8 0 3 3 9 8 8 7 4 9 8 9 5 . \n \n To compute the n th term in the F ib on acci sequence , you can use a loop to iterate through the terms and update the value of ph i for each iteration . Here ' s an example in Python : \n ``` python \n def fib on acci ( n ): \n ph i = ( 1 . 0 + math . sqrt ( 5 . 0 )) / 2 . 0 \n a , b = 0 , 1 \n result = [] \n for i in range ( n ): \n result . append ( a ) \n a , b = b , a + b \n return result \n ``` \n This function takes an integer ` n ` as input and returns a list of ` n ` F ib on acci numbers . You can call it with ` f ib on acci ( 1 0 )` to get the 1 0 th term in the F ib on acci sequence . </s>

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