EXPLANATION
Since we have the given sequence:
[tex]\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[/tex]
Computing the differences of all the adjacent terms:
[tex]d=a_n-a_{n-1}[/tex][tex]10-5=5,\: \quad \: 12-10=2,\: \quad \: 14-12=2,\: \quad \: 19-14=5[/tex]
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:
[tex]9-4.5=4.5,\: \quad \: 18-9=9,\: \quad \: 36-18=18[/tex]
The difference is not constant.
Therefore, the sequence is not an arithmetic one.
