SOLUTION: The sum of n terms of a certain series is {{{3n^2+10n}}} for all values of n. Fine the nth term and show that the series is an arithmetical progressim.

Question 1177181: The sum of n terms of a certain series is for all values of n. Fine the nth term and show that the series is an arithmetical progressim.
Answer by ikleyn(52834) (Show Source): You can put this solution on YOUR website!
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The sum of n terms of a certain series is 3n^2 + 10n for all values of n.
Find the nth term and show that the series is an arithmetical progression.
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If the sum of the first n terms of the sequence is given by the formula   = 3n^2 + 10n, then


 =  -  = (3n^2 + 10n) - ( 3(n-1)^2 + 10(n-1) ) =


           = 3n^2 + 10n - (3n^2 - 6n + 3 + 10n - 10) = 6n + 7.



The n-th term of the sequence is   = 6n + 7.


It is the arithmetic progression with the first term of 13 (at n= 1) and the common difference of 6.


The proof is completed.

Solved, answered, explained and completed.

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