Question

Find the next two numbers in the pattern.

7,−28,112,−448, 7,−28,112,−448,
1792,
, . . .

Answer 1

Let u_n be the n' th term of the sequence.



`u_1=7\\\\u_2=-28=-7\cdot4\\\\u_3=112=7 \cdot4^2\\\\u_4=-448=-7\cdot 64=-7\cdot 4^3\\\\u_5=1792=7 \cdot 4^4`

thus it is clear that:


`u_6=-7 \cdot 4^5=7168\\\\u_7=7\cdot 4^6=28,672`