Question

I need help with these. They are hard.

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Answer 1

Find the explicit from for the sequence
`t_n=t_(n-1)+4,t=6`:

`a_n=4n+2`

This next question I edited a bit. Your question just says find the four terms. I'm assuming they meant the first four. I also changed the c to an
`a`.

Find the first four terms of the sequence given by:
`a_n=n a_(n-1)-3,a_1=2`:

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense. I made my own interpretation of the problem based on my own mathematical experience.

Explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence. When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x | y

----------

1 6

2 10

3 14

4 18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is
`y-y_1=m(x-x_1)` where m is the slope and
`(x_1,y_1)` is a point on the line. You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

`y-6=4(x-1)`

`y=6+4(x-1)` :I added 6 on both sides here.

`y=6+4x-4` :I distribute here.

`y=4x+2` :This is what I get after combining like terms.

So
`a_n=y` and
`x=n` so you have:

`a_n=4n+2`

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The first four terms of this sequence will be given by:

`a_1,a_2,a_3,a_4`

`a_1=2` so it is between choice a, c, and d.

`a_n=na_(n-1)-3`

To find
`a_2` replace n with 2:

`a_2=2a_(1)-3`

`a_2=2(2)-3`

`a_2=4-3`

`a_2=1`

So we have to go another further the only one that has first two terms 2,1 is choice a.