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

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