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Re: A sequence of numbers contains terms
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22 May 2024, 19:36
Since \(t_9 = t_7 + t_8\), we need to use substitution and algebra to find \(t_7\).
We're given that \(t_5 = 18\). We aren't given what \(t_4\) is, but we can treat it as an unknown variable for now.
\(t_6 = t_4 + t_5 = t_4 + 18\)
\(t_7 = t_5 + t_6 = 18 + (t_4 + 18) = t_4 + 36\)
\(t_8 = t_6 + t_7 = (t_4 + 18) + (t_4 + 36) = 2t_4 + 54\)
Given that \(t_8 = 76\), solve for \(t_4\):
\(2t_4 + 54 = 76\)
\(t_4 = 11\)
Substitute \(t_4 = 11\) back in to find \(t_7\):
\(t_7 = 11 + 36 = 47\)
Now we can calculate \(t_9\):
\(t_9 = t_7 + t_8 = 47 + 76 = 123\)
Since 123 < 126, Quantity B is greater.