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vichka [17]
3 years ago
10

From the following information, reconcile the checkbook balance to the bank statement balance. Checkbook Balance $43,676.09 Bank

Balance 49,668.90 Outstanding Deposits 8,474.44 Outstanding Checks 12,322.25 Note Collected 2,160.00 Bank Service Charge 15.00
Mathematics
1 answer:
VashaNatasha [74]3 years ago
6 0

Answer:

To reconcile we need to match the checkbook balance with that of the bank balance :

Checkbook balance :

Initial checkbook balance = $43676.09

Note collected = $2160.00 , Bank Service Charge = $15

Final Checkbook Balance = Initial balance + Note collected - Service charge

                                            = 43676.09 + 2160 - 15

                                            = $45821.09

Bank balance :

Initial Bank balance = $49668.90

Outstanding deposits = $8474.44 , Outstanding checks = $12322.25

Final Bank Balance = Initial balance - Outstanding checks + Outstanding deposits

                                 = 49668.90 - 12322.25 + 8474.44

                                = $45821.09

So, both the checkbook balance and the bank balance are equal.

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<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

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.

<u>At, </u>

<u>n = 1</u>

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.

<u>At, </u>

<u>n = 2</u>

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.

<u>At, </u>

<u>n = 3</u>

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.

<u>At, </u>

<u>n = 4</u>

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'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

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

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