What is the 42 term where a1=-12 and a27=66

111

Step-by-step explanation:

a1 = -12

a27 = 66

Now using the formula  an = a1+(n-1)d we will find the value of d

here n = 27

a1 = -12

a27 = 66

Now substitute the values in the formula:

a27 = -12+(27-1)d

66= -12+(26)d

66 = -12+26 * d

66+12 = 26d

78 = 26d

now divide both the sides by 26

78/26= 26d/26

3 = d

Now put all the values in the formula to find the 42 term

an = a1+(n-1)d

a42 = -12 +(42-1)*3

a42 = -12+41 *3

a42 = -12+123

a42 = 111

Therefore 42 term is 111

Assuming it is arithmetic, the 42nd term is 111.

Assuming it is geometric, the conclusion says it isn't geometric.

Step-by-step explanation:

Let's assume arithmetic first.

Arithmetic sequences are linear. They go up or down by the same number over and over.  This is called the common difference.

We are giving two points on our line (1,-12) and (27,66).

Let's find the point-slope form of this line.

To do this I will need the slope.  The slope is the change of y over the change of x.

So I'm going to line up the points and subtract vertically, then put 2nd difference over 1st difference.

(1  , -12)

-(27,66)

------------

-26   -78

The slope is -78/-26=78/26=3.  The slope is also the common difference.

I'm going to use point and in the point-slope form of a line:

Distribute:

Subtract 12 on both sides:

So we want to know what y is when x=42.

So since the explicit form for this arithmetic sequence is

-----------------------------------------------------------------------------------------

Let's assume not the sequence is geometric. That means you can keep multiplying by the same number over and over to generate the terms given a term to start with.  That is called the common ratio.

The explicit form of a geometric sequence is .

We are given

so this means we have

.

We just need to find r, the common ratio.

If we divide 27th term by 1st term we get:

We are also given this ration should be equal to 66/-12.

So we have

.

So the given sequence is not geometric because we have an even powered r equaling a negative number.

80 the answer is 80

step-by-step explanation:

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.