Exercise 45 Page 592

We are told that the given sequence has eight terms, and are asked to evaluate the related series. Since the difference between consecutive terms is always the same, this is an arithmetic sequence. Given:& - 13, - 14.5, - 16, ... , - 23.5 Series:& (- 13)+ (- 14.5)+ (- 16)+ ... + (- 23.5) To calculate the value of the series, we will substitute a_1=- 13, a_n=- 23.5, and n=8 in the formula for the sum of a finite arithmetic series.

S_n=n/2( a_1+a_n )

SubstituteValues

Substitute values

S_8=8/2( - 13+( - 23.5) )

▼

Evaluate right-hand side

CalcQuot

Calculate quotient

S_8=4(- 13+(- 23.5))

AddNeg

a+(- b)=a-b

S_8=4(- 36.5)

Multiply

Multiply

S_8=-146