What is the sum of a 56–term arithmetic sequence where the first term is 6 and the last term is 391?

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Answer 1 · 2015-12-31T21:42:54

To begin, find the common ratio using the formula #t_n# = a + (n - 1)d

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

391 = 6 + (56 - 1)d
385 = 55d
7 = d

Now that we know the common ration we can proceed to find the sum using one of the sum formulas, as shown below.

#S_n# = #n/2#(#t_1# + #t_n#)

#S_56# = #56/2#(6 + 391)

#S_56# = 11 116

The sum of the 56 term is 11 116

Answer 2 · 2015-12-31T21:51:45

The sum is #56# times the average term

#56 xx (6+391)/2 = 11116#

The average term of an arithmetic sequence with finitely many terms is equal to the average of the extreme terms.

Then the sum is just the number of terms in the sequence multiplied by the average term.