Question

Last questions, plz help

I'm sry for all my pictures being in the wrong direction my phone was acting up so it wouldn't let me rotate​

Answer 1

9.
`a_n=7+6n`

10.
`a_n=a_(n-1)+7`

Explanation:

9. Given the sequence

`13, 19, 25, ...`

In this sequence,

`a_1=13\\ \\a_2=19\\ \\a_3=25\\ \\...`

Note that

`a_2-a_1=19-13=6\\ \\a_3-a_2=25-19=6,`

then the common difference in this sequence is
`d=6`

You have

`a_1=13\\ \\d=6,`

then the explicit formula is

`a_n=a_1+(n-1)d\\ \\a_n=13+(n-1)\cdot 6\\ \\a_n=13+6n-6\\ \\a_n=7+6n`

10. Given the sequence

`-10,-3, 4, 11, ...`

In this sequence,

`a_1=-10\\ \\a_2=-3\\ \\a_3=4\\ \\a_4=11\\ \\...`

Note that

`a_2-a_1=-10-(-3)=-10+3=-7\\ \\a_3-a_2=-3-4=-7\\ \\a_4-a_3=11-4=7,`

then the common difference in this sequence is
`d=7`

You have

`a_1=-10\\ \\d=7,`

then the recursive formula is

`a_n=a_(n-1)+d\\ \\a_n=a_(n-1)+7`