5-h> 2, 3, 4, 5 HELP QUICK

Find the nth term of the sequence 7,25,51,85,127

olya-2409 [2.1K]

Let a (n) denote the n-th term of the given sequence.

Check the forward differences, and denote the n-th difference by b (n). That is,

b (n) = a (n + 1) - a (n)

These so-called first differences are

b (1) = a (2) - a (1) = 25 - 7 = 18

b (2) = a (3) - a (2) = 51 - 25 = 26

b (3) = a (4) - a (3) = 85 - 51 = 34

b (4) = a (5) - a (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence b is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means b is an arithmetic sequence, and in particular follows the rule

b (n) = 18 + 8 (n - 1) = 8n + 10

for n ≥ 1.

So we have

a (n + 1) - a (n) = 8n + 10

or, replacing n + 1 with n,

a (n) = a (n - 1) + 8 (n - 1) + 10

a (n) = a (n - 1) + 8n + 2

We can solve for a (n) by iteratively substituting:

a (n) = [a (n - 2) + 8 (n - 1) + 2] + 8n + 2

a (n) = a (n - 2) + 8 (n + (n - 1)) + 2×2

a (n) = [a (n - 3) + 8 (n - 2) + 2] + 8 (n + (n - 1)) + 2×2

a (n) = a (n - 3) + 8 (n + (n - 1) + (n - 2)) + 3×2

and so on. The pattern should be clear; we end up with

a (n) = a (1) + 8 (n + (n - 1) + … + 3 + 2) + (n - 1)×2

The middle group is the sum,

$\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8$

so that

a (n) = a (1) + (4n ² + 4n - 8) + 2 (n - 1)

a (n) = 4n ² + 6n - 3

4 0

3 years ago

The altitude in feet of a plan minutes after is given by =3400 +600. How many after liftoff is the plane at an altitude of 21,00

nekit [7.7K]

A= 3400t + 600 | given formula
21000= 3400t + 600 | substitute the altitude into the formula
20400 = 3400 | subtract 600 from both sides
6 = t | divide both sides by 3400
6 minutes

3 0

2 years ago

Raul is practicing for baseball tryouts he wants to find how far he can hit a baseball he hits the ball 10 times and measures th

wel

Answer:

See Explanation

Step-by-step explanation:

Given

$n = 10$ --- Number of tryouts

Required

Determine the average distance

This question has missing details, as the distance he hits the ball in each tryout is not given. However, I'll give a general explanation.

The mean is calculated as:

$\bar x = \frac{\sum x}{n}$

$\sum x$ means the sum of the distance in each tryout.

Assume that the distance in the 10 tryouts are: $6, 8, 5, 9, 4, 5, 8, 7, 7, 6.$

So, the mean is:

$\bar x = \frac{6+ 8+ 5+ 9+ 4+ 5+ 8+ 7+ 7+ 6}{10}$

$\bar x = \frac{65}{10}$

$\bar x = 6.5}$

So, the average distance is 6.5

4 0

3 years ago

Read 2 more answers

What is synthetic division?

Cerrena [4.2K]

Answer:

A simplified method for dividing a polynomial by another polynomial of the first degree is synthetic division.

6 0

2 years ago

If the cash price of a truck is $25,000 and a business

olasank [31]

Answer:

500$

finaced= provide funding for

5 0

3 years ago