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# i don't understand. Help me. Respond on the first two please and thank you!

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The sum of the first n terms of a certain sequence is n(n+1)(n+2). Find the tenth term of the sequence.

In a sequence of ten terms, each term (starting with the third term) is equal to the sum of the two previous terms. The seventh term is equal to 6. Find the sum of all ten terms.

Given \( a_0 = 1 \) and \(a_1 = 5\) and the general relation \(a_n^2 - a_{n - 1} a_{n + 1} = (-1)^n\)
for \(n \ge 1\) find \(a_3\)

Feb 12, 2020
edited by Aopshelp  Feb 12, 2020
edited by Aopshelp  Feb 14, 2020

#1
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Feb 12, 2020
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Its not cheating if they understand the process and don't just copy the answer, Guest.

Feb 12, 2020
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The sum of the first n terms of a certain sequence is n(n+1)(n+2). Find the tenth term of the sequence.

The first term   is    1 ( 2) (3)  =  6  =  6(1)

The sum of the first two terms  =  2 (3) ( 4)  = 24...so   the second term  =  18  =  6(3)

The sum of the first three terms =  3 * 4 * 5  = 60.....so the third term =  36 = 6(6)

The sum of the first four terms =  4 * 5 *6  =  120....so....the fourth term = 60  = 6(10)

So....it appears that the  nth term  =   6 * nth triangular number  =  6 * n (n + 1) / 2

So....the 10th term is   6 * (10) ( 11)  / 2  =   30 * 11  =  330   Feb 12, 2020