The sum of 40 numbers in an arithmetic sequence is 8000. If the first number is the sequence is 83, what is the last number?

1 Answer
Mar 8, 2016

Answer:

#317#

Explanation:

In an arithmetic sequence the difference between consecutive members is constant. Therefore the sequence is
#83, 83+d, 83+2d,.....83+39d#

The #i#th member is #83+(i-1)d#

As shown on Arithmetic Sequences the formula for the sum of members is
#sum_0^(n-1) (a+kd) = n/2*(2a+(n-1)d)#

In this case
#sum_0^39 = 40/2*(2*83+39*d) = 8000#
#166+39d = 400#
#39d= 234#

#d=234/39 = 6#

The #40#th number is therefore #83 +39*6 = 317#