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Helen [10]
3 years ago
14

Find the exact sum of the arithmetic series 6+3.8+⋯−29.2

Mathematics
1 answer:
matrenka [14]3 years ago
5 0

Answer:

-197.2

Step-by-step explanation:

Since it is arithmetic series, first find the difference d between the two know series.

3.8 - 6 = - 2.2

d = -2.2

a = 6

Tn = -29.2

Looking for the n term, use the linear method.

Tn = a+( n - 1)d

Substitute all the parameters

-29.2 = 6+( n - 1 ) -2.2

-29.2 = 6 - 2.2n + 2.2

- 29.2 = 8.2 - 2.2n

-29.2 - 8.2 = - 2.2n

-37.4 = -2.2n

n = 37.4/ 2.2

n = 17 terms.

To Find the exact sum of the arithmetic series, use the sum formula below

Sm = n/2( 2a + (n - 1)d)

Sm = 17/2( 2 × 6 + ( 17 - 1 ) -2.2

Sm = 17/2(12 - 35.2)

Sm = 8.5( - 23.2)

Sm = - 197.2

Therefore, the exact sum of the arithmetic series is -197.2

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Step-by-step explanation:

15 x 3 = 45 + 3 = 48/15

then 4 + 5 = 20 + 2 = 22/5

22/5 + 48/15 = ?

find the common denominator  

15 ÷ by 3  so you do the same to the numerator so, 48 ÷ 3 = 16

then keep the 22 and 16 and put it as 16/5 and 22/5 and add them to get 38/5

hope this helps

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To find the measure of the windmill's blade:

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The correct question is given below:

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