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David is writing an explicit function for the arithmetic sequence:10,13,16,19,10, 13, 16, 19, \dots\newlineHe comes up with s(n)=7+3n.s(n) = 7 + 3n. What domain should David use for ss so it generates the sequence?\newlineChoose 11 answer:\newline(A) n0n \geq 0 where nn is an integer\newline(B) n0n \geq 0 where nn is any number\newline(C) n1n \geq 1 where nn is an integer\newline(D) n1n \geq 1 where nn is any number

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Q. David is writing an explicit function for the arithmetic sequence:10,13,16,19,10, 13, 16, 19, \dots\newlineHe comes up with s(n)=7+3n.s(n) = 7 + 3n. What domain should David use for ss so it generates the sequence?\newlineChoose 11 answer:\newline(A) n0n \geq 0 where nn is an integer\newline(B) n0n \geq 0 where nn is any number\newline(C) n1n \geq 1 where nn is an integer\newline(D) n1n \geq 1 where nn is any number
  1. Identify First Term: Identify the first term of the sequence using s(n)=7+3ns(n) = 7 + 3n. Calculate s(1)s(1):s(1)=7+3×1=10s(1) = 7 + 3 \times 1 = 10.
  2. Check Match: Check if s(1)s(1) matches the first term of the sequence (1010): Sequence starts at 1010, and s(1)=10s(1) = 10. This confirms that the sequence starts at n=1n = 1.
  3. Determine Nature of nn: Determine the nature of nn (integer or any number) by checking subsequent terms:\newlineCalculate s(2)=7+3×2=13s(2) = 7 + 3\times2 = 13, which matches the second term of the sequence. This pattern continues with integer values of nn.
  4. Confirm Non-Integer Values: Confirm that non-integer values of nn do not fit the sequence:\newlineCalculate s(1.5)=7+3×1.5=11.5s(1.5) = 7 + 3 \times 1.5 = 11.5, which does not appear in the sequence. Thus, nn must be an integer.

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