What is the next number in the pattern: 2, 7, 26, 101, 400?

the\ sequence\ can\ be\ determined\ recursively:\\\\ \left \{ {\big{a_1=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop\big {a_{n+1}=4\cdot a_n-n}} \right. \\\\\\a_6=4\cdot a_5-5=4\cdot400-4=1600-5=1595\\\\Ans.\ the\ nxt\ term\ is\ 1595.

Answered by kate200468 | 2024-06-10

2x4-1 7x4-2 26x4-3 101x4-4 400x4-5 and so on . . just do the math.

Answered by cutiepie42 | 2024-06-10

The next number in the sequence 2, 7, 26, 101, 400 is 1595, derived from the relation a n + 1 ​ = 4 ⋅ a n ​ − n . This sequence pattern involves multiplying the previous term by an increasing integer and then adjusting it by adding or subtracting a specific value.
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Answered by kate200468 | 2024-10-31