Question

mr. jones asks his students to generate the next two numbers in the sequence beginning -5.5, 11, .... taquan suggests that the sequence is geometric and the next two numbers are -22 and 44. julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44. which best explains which student is correct? taquan is correct. when the signs change in a sequence, the sequence is geometric. each successive term is generated by multiplying by -2. julia is correct. when the numbers alternate between decimals and whole numbers, the sequence is arithmetic. each successive term is generated by adding 16.5. both students could be correct about the types of possible sequences. however, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways. both students could be correct. because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

Explanation:

Given only two - terms (-5.5 and 11) in a sequence, we can consider both arithmetic and geometric possibilities. For a geometric sequence, the common ratio $r=\frac{11}{- 5.5}=-2$. For an arithmetic sequence, the common difference $d = 11-(-5.5)=16.5$. Just with two terms, we can find a common ratio for a geometric sequence and a common difference for an arithmetic sequence.

Answer:

Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.