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DiKsa [7]
3 years ago
7

What can you say about the sum of consecutive odd numbers starting with 1? that is, evaluate 1, 1c3, 1c3c5, 1c3c5c7, and so on,

and formulate a conjecture?
Mathematics
1 answer:
Mice21 [21]3 years ago
4 0

Let us add consecutive odd numbers and try to find any relationship.

1. 1

2. 1+3 = 4 ( square of 2 i.e 2^{2} )

3. 1+3+5 = 9 ( 3^{2} )

4.  1+3+5+7 =  16 (4^{2} )

5. 1+3+5+7+9 = 25 (5^{2} )

6. 1+3+5+7+9+11 = 36 ( 6^{2} )

7. 1+3+5+7+9+11+13 = 49 (7^{2} )

If we notice, the sum of the consecutive odd integers in each case is equal to the square of the place where it lies. For example, the sum of numbers in seventh place is equal to 7^{2}. The sum of the numbers in the fifth line is equal to 5^{2}.

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USPshnik [31]

Answer:

  • $17,500 at 8%
  • $17,500 at 14%

Step-by-step explanation:

The fraction that needs to be invested at the higher rate is ...

  (11% - 8%)/(14% -8%) = 3%/6% = 1/2

Half the money should be invested at each of the rates:

  $17,500 for 8% return

  $17,500 for 14% return.

_____

If you let x represent the amount at the higher rate, then the total return is ...

  14%x + 8%(35000 -x) = 11%(35000)

  (14% -8%)x = (11% -8%)(35000) . . . . subtract 8%·35000

  x = (11% -8%)/(14% -8%)×35000 . . . . divide by the coefficient of x

Note that this formula is exactly the one we started with, above.

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Step-by-step explanation:

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