Question

What is the sum of the arithmetic sequence -10,-15,-20,......,-100? Solve using the equation sn=d/2n^2+(f-d/2)n or n/2(x1+xn)

Answer 1

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A.P = -10,-15,-20,......,-100

a = first term = -10

d = common difference = -15-(-10) = -15+10 = -5

a.n = last term = -100

First find value of 'n'

Using a.n = a+(n-1)d

-100 = -10 + (n-1)(-5)

-100+10 = (n-1)(-5)

-90 = -5(n-1)

n-1 = -90/-5

n-1 = 18

n = 19

Sn = n/2(a+l). ( l is the last term i.e a.n)

= 19/2(-10+(-100))

= 19/2(-110)

= 19(-55)

= -1045

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