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Write the first five terms of a sequence. Write both an explicit formula and a recursive formula for a general term in the sequence. recursive formula for arithmetic sequence recursive formula for geometric sequence how to write a recursive formula recursive formula calculator arithmetic sequence formula calculator geometric sequence formula recursive sequence write the first five terms of the arithmetic sequence Report inappropriate predictions

Respuesta :

9, Β  Β 12, Β  Β 19, Β  Β 30, Β  Β ...

Therefore the whole formula for the nthΒ term is;

2n^2Β + 3n - 10

Answer with explanation:

β‡’Arithmetic Sequence

Β  Β  11,21,31,41,51,......

First term[tex]a_{1}[/tex] =11

Common Difference(d)=21-11=10

Β  [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]

β‡’Geometric Sequence

Β 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]

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