Question

Calculate s75 for the arithmetic sequence defined by

Answer 1

The formula of a sum of an arithmetic sequence:

$S_n=\dfrac{a_1+a_n}{2}\cdot n$

We have n = 75 and $a_n=67-2n$.

Calculate the first and seventy-fifth term:

$a_1=67-2(1)=67-2=65\\\\a_{75}=67-2(75)=67-150=-83$

Substitute:

$S_{75}=\dfrac{65+(-83)}{2}\cdot75=\dfrac{-18}{2}\cdot75=-9\cdot75=-675$

Answer: -675

Answer 2

Answer:

-675

Step-by-step explanation:

The first term a1  = 67 - 2 = 65

The common difference (d) = -2

sn = (n/2)[2a1 + (n-1)d]  so

s75 = (75/2)[2*65 + (75-1)*-2)]

= -675