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bazaltina [42]
3 years ago
11

12. The sum of four consecutive numbers in A.P. is 32 and the ratio of the product of the first and last terms to the product of

two middle terms is 7:15. Find the number.
Mathematics
1 answer:
Tomtit [17]3 years ago
8 0

Answer:

2, 6, 10, 14

or

14, 10, 6, 2.

Step-by-step explanation:

Let the four consecutive numbers in A.P. be a - 3d, a - d, a + d, a + 3d

According to the first condition:

a - 3d + a - d + a + d + a + 3d =32

4a = 32

a = 32/4

a = 8

According to the second condition:

\frac{(a - 3d)(a + 3d)}{(a - d)(a + d)}  =  \frac{7}{15}  \\  \\  \frac{ {a}^{2} - (3d)^{2}  }{ {a}^{2} -  {d}^{2}  }  =  \frac{7}{15}  \\  \\  \frac{ {a}^{2} - 9d^{2}  }{ {a}^{2} -  {d}^{2}  }  =  \frac{7}{15}  \\  \\  \frac{ {8}^{2} - 9d^{2}  }{ {8}^{2} -  {d}^{2}  }  =  \frac{7}{15}  \\  \\ \frac{ 64 - 9d^{2}  }{ 64 -  {d}^{2}  }  =  \frac{7}{15}  \\  \\ 15(64 - 9 {d}^{2} ) = 7(64 -   {d}^{2} ) \\  \\ 960 - 135 {d}^{2}  = 448 - 7 {d}^{2}  \\  \\ 960 - 448 = 135 {d}^{2}  - 7 {d}^{2}  \\  \\ 512 = 128 {d}^{2}  \\  \\  {d}^{2}  =  \frac{512}{128}  \\  \\  {d}^{2}  = 4 \\  \\ d =  \pm 2 \\  \\ when \: d = 2 \\ a - 3d = 8 - 3 \times 2 = 8 - 6 = 2 \\ a - d = 8 - 2 = 6 \\ a + d = 8 + 2 = 10 \\ a + 3d = 8 + 3 \times 2 = 8 + 6 = 14 \\\\ when \: d =  - 2 \\ a - 3d = 8 - 3 \times ( -2 ) = 8  +  6 = 14 \\ a - d = 8 -( -  2 )= 8 + 2 = 10 \\ a + d = 8 + ( - 2 )= 8 - 2 = 6\\ a + 3d = 8 + 3 \times ( - 2 )= 8  -  6 = 2 \\

Thus the four consecutive numbers of the A. P. are 2, 6, 10, 14 or 14, 10, 6, 2.

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<A = 30

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Step-by-step explanation:

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on her first day of work, mia sold one straw hat. on day two, she sold three straw hats. on day three, she sold five straw hats,
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If Mia sold 2 more hats on each suceeding day, after working 40 days it is expected Mia had sold a total of 1523 hats.

<h3>How many hats will Mia sell everyday?</h3>

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You can notice the number of hats she will sell follow a pattern as there are only sequential odd numbers.

<h3>How many hats will Mia sell in total?</h3>

By following the sequence let's add the hats she will sell everyday:

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Learn more about sums in: brainly.com/question/13013054

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