Respuesta :
9, 12, 19, 30, ...
Therefore the whole formula for the nth term is;2n^2 + 3n - 10
Answer with explanation:
⇒Arithmetic Sequence
11,21,31,41,51,......
First term[tex]a_{1}[/tex] =11
Common Difference(d)=21-11=10
[tex]\rightarrow a_{n}=a_{n-1}+10---{\text{Recursive formula}}\\\\\rightarrow a_{n}=a_{1}+(n-1)d\\\\a_{n}=11+(n-1)\times 10\\\\a_{n}=10n+1---{\text{Explicit formula}[/tex]
⇒Geometric Sequence
First five terms of the sequence are
[tex]4,4^2,4^3,4^4,4^5,.....\\\\\text{First term}=a_{1}=4\\\\ \text{Common ratio},r=\frac{a_{2}}{a_{1}}\\\\r=\frac{4^2}{4}\\\\r=4\\\\a_{n}=4\times a_{n-1}---\text{Recursive formula}\\\\a_{n}=a_{1}\times r^{n-1}\\\\a_{n}=4\times 4^{n-1}\\\\a_{n}=4^{1+n-1}\\\\a^n=4^n-----\text{Explicit formula}[/tex]
