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03-03-2018
Mathematics

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Use inductive reasoning to find the next term in the sequence 1, 2, 4, 7, 11, 16… what is the next term?
a. 18
b. 19
c. 22
d. 26

Respuesta :

03-03-2018

Hello,

[tex]u_1=1\\ u_2=2\\ u_3=4\\ u_4=7\\ u_5=11\\ u_6=16\\ u_2-u_1=2-1=1\\ u_3-u_2=4-2=2\\ u_4-u_3=7-4=3\\ u_5-u_4=11-7=4\\ u_6-u_5=16-11=5\\ ... u_n-u_{n-1}=n-1\\ \boxed{u_n=u_{n-1}+n-1}\\ u_7=u_6+(7-1)=16+6=22\\ [/tex]

Answer C

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