Answer :
The correct function that produces the given sequence (26, 35, 44, 53, 62) for n: {1, 2, ..., n} is C: f(n) = 9n + 17. This is determined by observing the constant difference of 9 between consecutive terms and testing the given options by substituting n=1 into them.
The first 5 numbers of the sequence are 26, 35, 44, 53, 62. To determine which function produces this sequence for n: \{1, 2, ..., n\}, we will calculate the difference between consecutive terms in the sequence. Observing the sequence, each term increases by 9 from the previous term (35-26=9, 44-35=9, and so on).
We can test each option by substituting n = 1 to see if it produces the first term of the sequence (26). Starting with option A, f(n) = 17 - 9n, and substituting n = 1, we get 17 - 9(1) = 8, which does not match the first term of the sequence. Therefore, option A is not correct.
Continuing to option B, An = 9n + 26, let's substitute n = 1, we get 9(1) + 26 = 35, which does not match the first term of the sequence, so option B is not correct either.
Moving to option C, f(n) = 9n + 17, substituting n = 1, we get 9(1) + 17 = 26, which does match the first term of the sequence. Testing the second term for when n = 2, we get 9(2) + 17 = 35, which matches the second term of the given sequence as well. Testing the remaining terms would further confirm that option C is indeed the correct function.
Lastly, option D, An = 26 - 9n, is clearly not correct as it would give decreasing values which do not match the increasing sequence provided.
Therefore, the correct function that generates the given sequence is C: f(n) = 9n + 17.
The function that produces the sequence with n: [1,2,...,] is "f(n) = 9n + 17" (Option C). See the explanation below.
What is the explanation to the above answer?
Note that we want a function which produces the sequence 26, 35, 44, 53, 62, if {1, 2, 3......n} is plugged into it.
Lets test the function with the integer 1:
9 (1) + 17
= 9+ 17
= 26 [Correct]
Lets true 2;
9(2) + 17
= 18 + 17
= 35 [Correct]
Lets try 3;
9 (3) + 17
= 27 + 17
= 44 [Correct]
Hence the selected function (Option C) is correct.
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