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The sequence a1, a2,a3...an is defined such that an=an-1+9+n for all n
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31 Mar 2021, 05:30
31 Mar 2021, 05:30
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The sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\) is defined such that \(a_n=a_{n-1}+9+n\) for all \(n>1\). If \(a_1=10\), what is the value of \(a_{11}\)?
(A) 150
(B) 155
(C) 160
(D) 165
(E) 170
(A) 150
(B) 155
(C) 160
(D) 165
(E) 170
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The sequence a1, a2,a3...an is defined such that an=an-1+9+n for all n
[#permalink]
31 Mar 2021, 09:47
31 Mar 2021, 09:47
GeminiHeat wrote:
The sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\) is defined such that \(a_n=a_{n-1}+9+n\) for all \(n>1\). If \(a_1=10\), what is the value of \(a_{11}\)?
(A) 150
(B) 155
(C) 160
(D) 165
(E) 170
(A) 150
(B) 155
(C) 160
(D) 165
(E) 170
\(a_n = a_{n-1} + 9 + n\)
\(a_2 = a_1 + 9 + 2 = 10 + 9 + 2 = 21\)
\(a_3 = a_2 + 9 + 3 = 21 + 9 + 3 = 33\)
\(a_4 = a_4 + 9 + 4 = 33 + 9 + 4 = 46\)
\(a_5 = a_4 + 9 + 5 = 46 + 9 + 5 = 60\) ...
We have a pattern: \(10, (10 + 11), (10 + 11 + 12), (10 + 11 + 12 + 13), (10 + 11 + 12 + 13 + 14), .....\)
So \(a_{11} = 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20\)
Sum \(= \frac{n}{2}(L + F) = \frac{11}{2}(20 + 10) = (11)(15) = 165\)
Hence, option D
Re: The sequence a1, a2,a3...an is defined such that an=an-1+9+n for all n
[#permalink]
03 Apr 2021, 05:38
03 Apr 2021, 05:38
any shortcut, its look like time consuming?
