Identify the pattern in the following sequence. 77, 221, 405, 629, 893 What is the next number in the sequence?
1197
We are given the sequence 77, 221, 405, 629, 893 and must find the next term by identifying the underlying pattern.
First, find the differences between consecutive terms.
\(221-77=144\), \(405-221=184\), \(629-405=224\), \(893-629=264\).
The first differences are 144, 184, 224, 264, which themselves increase by a constant 40 each time (second difference \(=40\)).
So the next first difference is \(264+40=304\).
Therefore the next term \(=893+304=1197\).
The value 1197 matches the second option.
The correct answer is 1197.
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