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The term-to-term rule for a sequence is 'subtract \( k \).' The 1st term of the sequence is 40. The 4th term of the sequence is 35.5.

a) Find the 2nd and 3rd terms of the sequence.
\[ 40, \_, \_, 35.5 \]

b) Find the first negative term in the sequence.

Answer :

Final answer:

In a sequence with the first term 40 and term-to-term rule 'subtract k', where 'k' equals (40 - 35.5) / 3 = 1.5, the 2nd and 3rd terms of the sequence are 38.5 and 37, respectively. The first negative term would occur at the 27th term.

Explanation:

This problem is about the patterns within a mathematical sequence. The rule for this sequence is 'subtract k'. We know that the 1st term is 40 and the 4th term is 35.5.

This means that 'k' has to be equal to the difference between 4th term and the 1st term divided by 3 (as there are three differences between 4 numbers), so 'k' equals to (40 - 35.5) / 3 = 1.5. Therefore, the 2nd term would be 40 - 1.5 = 38.5 and the 3rd term would be 38.5 - 1.5 = 37 .

To find the first negative term, we need to find when the sequence reaches below zero. This can be done by dividing the first term by 'k' and rounding up to the nearest whole number, because we are looking for the term number, which has to be a whole number. 40 / 1.5 = 26.67. So we round up to 27, meaning the 27th term would be the first negative term in the sequence.

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