How do you find the sum of each arithmetic series #50+44+38+...+8#?

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Answer 1 · 2016-11-05T09:22:28

There are 8 terms and the sum, #S_8 =232#

#50+44+38 +.....+8" "larr# (each new term is 6 less.)

In the series given, we have the following information:

#a_1 = 50, d= -6 and T_n = 8#

We need to know how many terms there are first. (Find #n#)
We can see that the last term is 8, but which term is it?

#T_n = a + d(n-1)#

#8 = 50 -6(n-1)#

#8 = 50-6n +6#

#6n = 54-6#

#6n = 48#

#n =8#

There are 2 formulae which we can use, but as we know the last term, let's use:

#S_n = n/2(a+l)#

#S_8 = 8/2(50+8)#

#S_8 = 4xx58#

#S_8 =232#