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.
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-> 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.
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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(52831) (Show Source):
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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.
