What is the sum of the arithmetic sequence 4, 11, 18 …, if there are 26 terms?

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Answer 1 · 2015-06-11T21:56:41

This sequence can be written as:

#a_(n+1) = a_n + 7#
#AA n in [0,26]# (for all #n# from #0# to #26#, inclusive)
with #a_0 = 4#.

You can also write this as:

#sum_(n=1)^(26) 7n - 3#

...which is easier to solve, even by hand.

#4 + 11 + 18 +...#

#= (7(1) - 3) + (7(2) - 3) + (7(3) - 3) + ...#

#= 7(1) + 7(2) + 7(3) + ... - 3 - 3 - 3 - ...#

#= 7(1+2+3+...+26) - 3(26)#

#= 7((26*27)/2) - 78#

#= 7(13*27) - 78#

#= 7(3*27 + 10*27) - 78#

#= 7(351) - 78#

#= 2457 - 78#

#= 2379#

So, in general:

#sum_(n=1)^(N) an pm b = a/2*n(n+1) pm bn#

#7/2 * (26*27) - 3*26 = 2379#