Question

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

Answer 1

9, 12, 19, 30, ...

Therefore the whole formula for the nth term is;

2n^2 + 3n - 10

Answer 2

Answer with explanation:

⇒Arithmetic Sequence

11,21,31,41,51,......

First term
`a_(1)` =11

Common Difference(d)=21-11=10

`\rightarrow a_(n)=a_(n-1)+10---{\text{Recursive formula}}\\\\\rightarrow a_(n)=a_(1)+(n-1)d\\\\a_(n)=11+(n-1)* 10\\\\a_(n)=10n+1---{\text{Explicit formula}`

⇒Geometric Sequence

First five terms of the sequence are

`4,4^2,4^3,4^4,4^5,.....\\\\\text{First term}=a_(1)=4\\\\ \text{Common ratio},r=(a_(2))/(a_(1))\\\\r=(4^2)/(4)\\\\r=4\\\\a_(n)=4* a_(n-1)---\text{Recursive formula}\\\\a_(n)=a_(1)* r^(n-1)\\\\a_(n)=4* 4^(n-1)\\\\a_(n)=4^(1+n-1)\\\\a^n=4^n-----\text{Explicit formula}`