All categories

2 years ago

What is a31 of the arithmetic sequence for which a5=12.4 and a9=22.4

1 answer:

6 0

For the arithmetic sequence
a₁, a₂, a₃, ...,
the n-th term is
$a_{n}=a_{1}+(n-1)d$
where d = the common difference

Because a₅ = 12.4,
a₁ + 4d = 12.4 (1)
Because a₉ = 22.4,
a₁ + 8d = 22.4 (2)

Subtract (1) from (2).
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
d = 2.5
From (1),
a₁ = 12.4 - 4*2.5 = 2.4

Therefore
a₃₁ = 2.4 + 30*2.5 = 77.4

Answer: a₃₁ = 77.4

You might be interested in

Prove the following using a proof by contradiction:The average of four real numbers is greater than or equal to at least one of

skelet666 [1.2K]

Answer:

By contradiction it can be proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

Step-by-step explanation:

Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.

As a result, we prove the fact.

Here, let the four number be:

$p, q, r, s$

The average will be Sum of all numbers divided by count of numbers.

$\dfrac{p+ q+ r+ s}4$

Now, let us assume the opposite that the average is less than all the numbers.

i.e.

$\dfrac{p+ q+ r+ s}4$

Now, let us add all of them:

$\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4$

Which can never be possible hence, our assumption is contradicted.

our assumption is wrong.

Therefore, by contradiction it is proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

8 0

2 years ago

A 3-column table with 6 rows. Column 1 is labeled Month with entries July, August, September, October, November, December. Colum

Orlov [11]

Answer:

I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.

Hope's this helps you.

6 0

2 years ago

Read 2 more answers

What is Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price pe

Shalnov [3]

Since we are finding the unit rate of the cost per comic, we will need to divide $5 by 20 comics which you will get 0.25 cents and divide $7.50 by 30 comics which you will also get 0.25 cents.Therefore, the unit rate and constant of proportionality is 0.25 cents.

8 0

2 years ago

Read 2 more answers

Find the values of x and y that satisfy the equation.<br><br> 4x+2i=8+yi<br> x= <br> and y=

stiks02 [169]

Answer:

The values of x and y that satisfy the equation are 2 and 2, respectively.

Step-by-step explanation:

Two complex numbers are identical if and only each pair of respective coefficients are identical on both sides. Then, we need to observe the following conditions:

Real component

$4\cdot x = 8$ (1)

Imaginary component

$2 = y$ (2)

The solution of this system of equations is $x = 2$ and $y = 2$ .

The values of x and y that satisfy the equation are 2 and 2, respectively.

5 0

2 years ago

Arrange the summation expressions in increasing order of their values.

dolphi86 [110]

∑ 4 * 5^(i-1) = 4 + 20 + 100 + 500 = 624
∑ 3 * 4^(i-1) = 3 + 12 + 48 + 192 + 768 = 1,023
∑ 5* 6^(i-1) = 5 + 30 = 35
∑ 5^(i-1) = 1 + 5 + 25 + 125 = 156
Answer:
∑ (i=1, 2) 5 * 6^(i-1) < ∑ (i=1, 4) 5^(i-1) < ∑ (i=1, 4) 4 * 5^(i-1) <
< ∑ (i=1, 5) 3 * 4^(i-1)

5 0

2 years ago

Read 2 more answers