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sergejj [24]
3 years ago
12

the third term of an arithmetic sequence is 24 and the fifth is 32 if the first term is a1. which is an equation nth term of the

sequence
Mathematics
2 answers:
const2013 [10]3 years ago
8 0
An = a1 + (n - 1)(d)
Where a1 is the first term and d is the common difference.
First find d, the common difference.
24, ____, 32
a3 a4 a5
Subtract 32-24 = 8
Subtract a5 - a3 = 2
Divide 8/2 = 4
d = 4
Use d and one of the values they give us to find a1.
a3 = 24
24 = a1 + (3 - 1)(4)
24 = a1 + 2(4)
24 = a1 + 8
Subtract 8 from both sides
16 = a1
an = 16 + (n - 1)(4)
Can also be written
an = 16 + 4n - 4
an = 4n + 12
Fudgin [204]3 years ago
6 0

Answer:

The nth term of the sequence is a_n=4n+12

Step-by-step explanation:

Given: a_3=24,\ \ a_5=32

First term: a_1

Formula:

a_n=a_1+(n-1)d

where, d is common difference

a_3=24

a_1+2d=24

a_1+4d=32

Subtract both equation

2d=32-24

2d=8

d=4

Put d=4 into a_1+2d=24

a_1+2(4)=24

a_1=16

Now, we will find nth term of the sequence.

a_n=16+(n-1)4

a_n=16+4n-4

a_n=4n+12

Hence, The nth term of the sequence is a_n=4n+12

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3 years ago
A taxicab charges $1.75 for the flat fee and $0.25 for each mile. write an inequality to determine how many miles eddie can trav
aev [14]

The correct option is a. $1.75 + $0.25x ≤ $15; x < 53 miles.

The inequality that represents given situation is $1.75 + $0.25x ≤ $15.

<h3>What is inequalities?</h3>

An inequality compares the two values to determine if one is less than, larger than, or simply simply equal to the other.

  • a ≠ b indicates that an is not equal to b.
  • a < b indicates that an is less than b.
  • The expression a > b indicates that an is greater than b. (those two are called as strict inequality)
  • a ≤ b signifies that an is less than or equal to b.
  • The expression a ≥ b denotes that an is greater than or equal to b.

Now for the given question;

A cab charges $1.75 for the flat fee.

And, the cab charges $0.25 for each mile.

Total amount spent by Eddie is 1$15.

So, first and foremost. Because you have to pay the fixed charge and then pay for x miles is $0.25.

Thus, (15-1.75) / 0.25 = 53.

Therefore, the inequalities which describes the given scenario is;

$1.75 + $0.25x ≤ $15

where, x < 53 miles.

To know more about the inequalities, here

brainly.com/question/11613554

#SPJ4

The correct question is-

A cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddie can travel if he has $15 to spend.

a. $1.75 + $0.25x ≤ $15; x ≤ 53 miles

b. $1.75 + $0.25x ≥ $15; x ≥ 53 miles

c. $0.25 + $1.75x ≤ $15; x ≤ 8 miles

d. $0.25 + $1.75x ≥ $15; x ≥ 8 miles

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