The first term of an arithmetic progression is 1.75 and the second term is 1.5. The sum of the first n terms is -n. Find the value of n.

Answer 1

n=23

a1 =1.75

a2 = 1.5

d=1.5-1.75 = -.25 = -1/4

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

sn = (n/2)(3.5 -.25(n-1)) =-n

3.5 - (n-1)/4 = -2

-(n-1)/4 = -5.5

-(n-1) = 4(-5.5)= -22

n-1 =22

n=23

an = a1 + d(n-1)

a23 = 1.75-.25(23-1) = 7/4 -22/4 = -15/4 = -3.75

s23 = 1.75+1.5+1.25+1+ ...-3.5-3.75 = -23

s23 =sum of 1st 23 terms of the arithmetic sequence

= 1.75 + 1.5 +1.25 + 1 + .75 +.5 + .25 + 0 - .25 - .5 - .75 - 1 - 1.25 - 1.5

-1.75 -2 -2.25 -2.5 -2.75 -3 -3.25 -3.5 -3.75

=-23

=-n