Step-by-step explanation
Since we have the given sequence:
![\mathrm{An\: arithmetic\: sequence\: has\: a\: constant\: d}if\mathrm{ference\: }_{\text{ }}d_{\text{ }}\mathrm{\: and\: is\: defined\: by}\: a_n=a_1+\mleft(n-1\mright)d]()
Computing the differences of all the adjacent terms:
![d=a_n-a_(n-1)](https://img.qammunity.org/2023/formulas/mathematics/college/vmnlzexui4d8na47c1wn9b8q483qe6kbuv.png)
![10-5=5,\: \quad \: 12-10=2,\: \quad \: 14-12=2,\: \quad \: 19-14=5](https://img.qammunity.org/2023/formulas/mathematics/college/q4ixfbo8nfyjh3gsym1i791ipvxfpfqx62.png)
The difference is not constant, thus the sequence is not arithmetic.
b) Applying the same reasoning to the second sequence:
4.5, 9,18,36
Computing the difference of all the adjacent terms:
![9-4.5=4.5,\: \quad \: 18-9=9,\: \quad \: 36-18=18](https://img.qammunity.org/2023/formulas/mathematics/college/8x1p9dt3l8i6jia7o6mniczkly1ik7nrih.png)
The difference is not constant.
Therefore, the sequence is not an arithmetic one.