the third graders collected 754 cans. Fourth Graders collected 592 cans. estimate how many more cans the third graders collected

A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

At,

n = 4

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

3 0

3 years ago

THIS IS URGENTE I AM BEING TIMED PLZ HELP, if you answer correct i will mark you brainlyist

RoseWind [281]

Answer:

5.85

Step-by-step explanation:

$40.95 / 7 =5.85

5 0

3 years ago

Kevin rented a truck for one day. there was a base fee of $17.99, and there was an additional charge of 95 cents for each mile d

Darina [25.2K]

Answer:

Step-by-step explanation:

Base fee = $17.99

Additional charge = $0.95 for each mile driven

If Kevin paid $157.64 when he returned the truck and we want to find out how many miles he drove the truck, step 1 would be to subtract the base fee.

157.65 - 17.99 = 139.65

This means that the remaining $139.65 is how much he paid for the miles he drove.

Since we know each mile costs $0.95.

Simply divide $139.65 by $0.95 to work out how many miles he drove.

Miles driven = 139.65 / 0.95 = ?

4 0

4 years ago

steve desposite $1800 per month in his saving bank account. If thi is 20% of the monthly income, find his monthly income

Vikki [24]

Step-by-step explanation:

Hey there!

The amount deposited= $1800

And it's just 20% of total monthly amount.

Let total amount be "x".

Then;

$1800 = 20% of X

$1800 = \frac{20}{100} \times x$

or, 180000= 20x

or, X = 180000=/20

Therefore, total monthly amount or income was $9000.

Hope it helps!

8 0

3 years ago

What is 9/10 of 7 inches

PSYCHO15rus [73]

It is equivalent to 16 cm

4 0

3 years ago