Mathematics, 10.10.2021 17:30 saramerguelo

Determine if each of the following sequences is arithmetic. If so, write Zrecursive rule and an explicit rule for the sequence. If not, explain why. (Lesson 4.2) 3. -8,-1, 6, 13... 4. 1, 8, 27,81...

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Answer from: zachisthequeen2002

9514 1404 393

3. yes: a[1] = -8, a[n] = a[n-1] +7; an = -8 +7(n -1)

4. no (no common difference)

Step-by-step explanation:

An arithmetic sequence is one in which each term has the same difference from the term before it.

3. -1 -(-8) = 7; 6 -(-1) = 7; 13 -6 - 7. The differences are all 7, so the terms have a common difference. This sequence is arithmetic.

The general form of the recursive rule for an arithmetic sequence with first term a1 and common difference d is ...

a[1] = a1; a[n] = a[n-1] +d . . . . . recursive rule

a[1] = -8; a[n] = a[n-1] +7

The general form of the explicit rule for an arithmetic sequence is ...

an = a1 +d(n -1)

an = -8 +7(n -1)

4. The differences are ...

8 -1 = 7; 27 -8 = 19; 81 -27 = 54 . . . the differences are not common

This sequences is not arithmetic.

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

the car was traveling 40 mph before it started skidding. ( 2 points ) 17. was the driver were her brakes working at 75% efficiency or better? ( 2 points ) yes 29.

step-by-step explanation:

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