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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

User Jtpereyda
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1 Answer

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Hello,


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\\

Answer C

User MinhNguyen
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