Find the exact sum of the arithmetic series

6+3.8+⋯−29.2

-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

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

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