Mathematics, 14.07.2020 18:01 harleyquinn1241

What is the nth term rule of the quadratic sequence below? 4,15,30,49,72,99,130,...

Answers: 1

Show answers

Answers

Answer from: rtorres3

The nth term rule of the quadratic sequence is $2n^{2} +5n-3$ .

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by = $an^{2}+bn+c$

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a = $\dfrac{4}{2}$ = 2

SO, the first term of the nth term rule equation is $an^{2}$ = $2n^{2}$ .

Now, in the term $2n^{2}$ , put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then $2n^{2}$ = $2 \times (1)^{2}$ = 2

If n = 2, then $2n^{2}$ = $2 \times (2)^{2}$ = 8

If n = 3, then $2n^{2}$ = $2 \times (3)^{2}$ = 18

If n = 4, then $2n^{2}$ = $2 \times (4)^{2}$ = 32

If n = 5, then $2n^{2}$ = $2 \times (5)^{2}$ = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is $2n^{2} +5n-3$ .

Answer from: Quest

answer: 34rtyj,jkhtyetwrhyjeuiejnbhdfknbkguxfrbhkfdbjvkmbd,kvbsd.kxjvbhjnfbgjxdfn

step-by-step explanation:

Which of the following describes the transformations performed on the object shown above? a. the o

Answer from: Quest

nada

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:30

We have enough material to build a fence around a station that has a perimeter of 180 feet the width of the rectangular space must be 3 1/4 feet what must the length be

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

The price of a visit to the dentist is calculated according to the formula 50+100n50+100n where nn is the number of cavities the dentist finds. on your last visit to the dentist, 22 cavities were found. what was the cost of your visit?

Answers: 2

Answer

Mathematics, 21.06.2019 22:30

Avery’s piggy bank has 300 nickels, 450 pennies, and 150 dimes. she randomly picks three coins. each time she picks a coin, she makes a note of it and puts it back into the piggy bank before picking the next coin.

Answers: 1

Answer

Mathematics, 22.06.2019 00:00

Astocks price gained 3% in april and 5% in may and then lost 4% in june and 1% in july during which month did the stocks price change the most

Answers: 1

Answer

You know the right answer?

What is the nth term rule of the quadratic sequence below? 4,15,30,49,72,99,130,......

Questions

Mathematics, 12.10.2020 22:01

Jill and Erika made 4 gallons of lemonade for their lemonade stand. How many quarts did they make? A .1 quart B .16 quarts C .20 quarts

Mathematics, 12.10.2020 22:01